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Transition probability estimates for subordinate random walks Math. Nachr. (IF 0.91) Pub Date : 2021-01-21 Wojciech Cygan; Stjepan Šebek
Let S n be a symmetric simple random walk on the integer lattice Z d . For a Bernstein function ϕ we consider a random walk S n ϕ which is subordinated to S n . Under a certain assumption on the behaviour of ϕ at zero we establish global estimates for the transition probabilities of the random walk S n ϕ . The main tools that we apply are a parabolic Harnack inequality and appropriate bounds for the
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Notes about s‐numbers for a Sobolev type embedding of order 4 and for a higher order integral operator Math. Nachr. (IF 0.91) Pub Date : 2021-01-18 Petr Gurka; Jan Lang
The main focus of this paper is on study of s‐numbers for a higher order Sobolev embedding on an interval and also for the corresponding Hardy‐type operator. Upper and lower estimates for approximation and Bernstein numbers are described and their relations with results for lower order Sobolev embeddings are discussed.
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On the dimension of self‐similar measures with complicated overlaps Math. Nachr. (IF 0.91) Pub Date : 2021-01-17 Balázs Bárány; Edina Szvák
In this paper, we investigate the Hausdorff dimension of the invariant measures of the iterated function system (IFS) { α x , β x , γ x + ( 1 − γ ) } . We provide an “almost every” type result by a direct application of the results of Feng and Hu [5] and Kamalutdinov and Tetenov [9].
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General approach to Köthe echelon algebras Math. Nachr. (IF 0.91) Pub Date : 2021-01-13 Tomasz Ciaś; Krzysztof Piszczek
We provide a study of Köthe sequence algebras. These are Fréchet sequence algebras which can be viewed as abstract analogoues of algebras of smooth or holomorphic functions. Of particular treatment are the following properties: unitality, m‐convexity, Q‐property and variants of amenability. These properties are then checked against the topological ( DN ) ‐(Ω) type conditions of Vogt–Zaharjuta. Description
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Multiple positive steady states of a diffusive predator‐prey model in spatially heterogeneous environments Math. Nachr. (IF 0.91) Pub Date : 2021-01-09 Biao Wang; Jianhua Wu
In this paper, we discuss a diffusive predator‐prey model with predator cannibalism in spatially heterogeneous environments. In contrast with spatially homogeneous environments, we find the dynamics of the model in spatially heterogenous environments is more complicated. For the spatially heterogeneous case, we could classify death rate of the predator into four different regions and demonstrate that
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Exponential stabilization of laminated beams with history memories Math. Nachr. (IF 0.91) Pub Date : 2021-01-07 B. Feng; D. S. Almeida Júnior; A. J. A. Ramos
In this paper we consider laminated beams modelled from the well established Timoshenko system, which is a structure given by two identical layers uniform on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. By using semi‐group approach, we prove the global well‐posedness of the system when a viscoelastic dissipation
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The Calderón–Zygmund estimates for a class of nonlinear elliptic equations with measure data Math. Nachr. (IF 0.91) Pub Date : 2021-01-07 Shuang Liang; Shenzhou Zheng
We study a class of nonlinear elliptic equations involving measure data − div A ( x , D u ) = μ in Ω , where μ is a Radon measure. Under the main assumption of A ( x , ξ ) that there exists a constant Λ > 0 such that | A ( x , ξ ) − A ( x 0 , ξ ) | ≤ Λ ( a ( x ) + a ( x 0 ) ) | x − x 0 | α ( | ξ | 2 + s 2 ) p − 1 2 , α ∈ ( 0 , 1 ] , where 0 ≤ a ( x ) ∈ L m ( Ω ) for some integrable index m > 1 , we
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Lp‐Estimates for the ∂¯b‐equation on a class of infinite type domains Math. Nachr. (IF 0.91) Pub Date : 2020-10-30 Tran Vu Khanh; Andrew Raich
We prove L p estimates, 1 ≤ p ≤ ∞ , for solutions to the tangential Cauchy–Riemann equations ∂ ¯ b u = ϕ on a class of infinite type domains Ω ⊂ C 2 . The domains under consideration are a class of convex ellipsoids, and we show that if ϕ is a ∂ ¯ b ‐closed (0,1)‐form with coefficients in L p , then there exists an explicit solution u satisfying ∥ u ∥ L p ( b Ω ) ≤ C ∥ ϕ ∥ L p ( b Ω ) . Moreover, when
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On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation Math. Nachr. (IF 0.91) Pub Date : 2020-11-03 Tomoyuki Nakatsuka
We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution { u , p } of the Navier–Stokes equation such that | ∇ j u ( t , x ) | = O ( | x | 1 − n − j ) and | ∇ j p ( t , x ) | = O ( | x |
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Nevanlinna and Carleson functions of analytic self‐maps on multiply‐connected domains Math. Nachr. (IF 0.91) Pub Date : 2020-11-10 Michał Rzeczkowski
In the paper we prove that the Nevanlinna counting function and the Carleson function of analytic self‐maps of finitely connected domains with smooth boundary are equivalent. Using this result we obtain the characterization of compact composition operators on Hardy–Orlicz spaces.
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Real hypersurfaces in the complex hyperbolic quadric with harmonic curvature Math. Nachr. (IF 0.91) Pub Date : 2020-11-01 Young Jin Suh
We give a classification of real hypersurfaces in the complex hyperbolic quadric Q m ∗ = S O 2 , m o / S O 2 S O m that have constant mean curvature and harmonic curvature.
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Nielsen's beta function and some infinitely divisible distributions Math. Nachr. (IF 0.91) Pub Date : 2020-12-28 Christian Berg; Stamatis Koumandos; Henrik L. Pedersen
We show that a large collection of special functions, in particular Nielsen's beta function, are generalized Stieltjes functions of order 2, and therefore logarithmically completely monotonic. This includes the Laplace transform of functions of the form x f ( x ) , where f is itself the Laplace transform of a sum of dilations and translations of periodic functions. Our methods are also applied to ratios
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Heat kernels and regularity for rough metrics on smooth manifolds Math. Nachr. (IF 0.91) Pub Date : 2020-09-28 Lashi Bandara; Paul Bryan
We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Hölder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.
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Degeneration of torsors over families of del Pezzo surfaces Math. Nachr. (IF 0.91) Pub Date : 2020-10-09 Ulrich Derenthal; Norbert Hoffmann
Let S be a split family of del Pezzo surfaces over a discrete valuation ring such that the general fiber is smooth and the special fiber has ADE ‐singularities. Let G be the reductive group given by the root system of these singularities. We construct a G‐torsor over S whose restriction to the generic fiber is the extension of structure group of the universal torsor. This extends a construction of
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Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I Math. Nachr. (IF 0.91) Pub Date : 2020-10-05 Adrian Vasiu
We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic (0, p). As a first application we provide a smooth solution (answer) to a conjecture (question) of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic (0, p) of integral canonical
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Subelliptic Gevrey spaces Math. Nachr. (IF 0.91) Pub Date : 2020-12-02 Véronique Fischer; Michael Ruzhansky; Chiara Alba Taranto
In this paper, we define and study Gevrey spaces associated with a Hörmander family of (globally defined) vector fields and its corresponding sub‐Laplacian. We show some natural relations between the various Gevrey spaces in this setting on general manifolds, and more particular properties on Lie groups with polynomial growth of the volume. In the case of the Heisenberg group and of S U ( 2 ) , we
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Series representations in spaces of vector‐valued functions via Schauder decompositions Math. Nachr. (IF 0.91) Pub Date : 2020-11-30 Karsten Kruse
It is a classical result that every C ‐valued holomorphic function has a local power series representation. This even remains true for holomorphic functions with values in a locally complete locally convex Hausdorff space E over C . Motivated by this example we try to answer the following question. Let E be a locally convex Hausdorff space over a field K , let F ( Ω ) be a locally convex Hausdorff
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Feller semigroups and degenerate elliptic operators III Math. Nachr. (IF 0.91) Pub Date : 2020-11-30 Kazuaki Taira
This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups in the characteristic case via the Fichera function. Probabilistically, our result may be stated as follows: We construct a Feller semigroup corresponding to such a diffusion phenomenon that a Markovian particle moves continuously in the interior of the state space, without reaching the boundary
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Ideal triangulations of 3‐manifolds up to decorated transit equivalences Math. Nachr. (IF 0.91) Pub Date : 2020-11-29 Riccardo Benedetti
We consider 3‐dimensional pseudo‐manifolds M ̂ with a given set of marked point V such that M ̂ ∖ V is the interior of a compact 3‐manifold with boundary M. An ideal triangulation T of ( M ̂ , V ) has V as set of vertices. A branching ( T , b ) enhances T to a Δ‐complex. Branched triangulations of ( M ̂ , V ) are considered up to the b‐transit equivalence generated by isotopy and ideal branched moves
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The Fitting subgroup, p‐length, derived length and character table Math. Nachr. (IF 0.91) Pub Date : 2020-11-26 Neda Ahanjideh
For a character χ of a finite group G, the number χ c ( 1 ) = [ G : ker χ ] χ ( 1 ) is called the codegree of χ. Let N be a normal subgroup of G and set Irr ( G | N ) = Irr ( G ) − Irr ( G / N ) . Let p be a prime. In this paper, we first show that if for two distinct prime divisors p and q of | N | , p q divides none of the codegrees of elements of Irr ( G | N ) , then Fit ( N ) ≠ { 1 } and N is either
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Generalized fractional integral operators on Orlicz–Hardy spaces Math. Nachr. (IF 0.91) Pub Date : 2020-11-20 Ryutaro Arai; Eiichi Nakai; Yoshihiro Sawano
The generalized fractional integral operators are shown to be bounded from an Orlicz–Hardy space H Φ ( R n ) to another Orlicz–Hardy space H Ψ ( R n ) , where Φ and Ψ are generalized Young functions. The result extends the boundedness of the usual fractional integral operator I α from H p ( R n ) to H q ( R n ) for α , p , q ∈ ( 0 , ∞ ) and − n / p + α = − n / q , which was proved by Stein and Weiss
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Dichotomy and μ‐pseudo almost automorphic solutions for delayed partial functional differential equations in admissible spaces Math. Nachr. (IF 0.91) Pub Date : 2020-11-12 Chiraz Jendoubi
We prove the existence and uniqueness of μ‐pseudo almost automorphic solution for a delayed non‐autonomous partial functional differential equation in the exponential dichotomic case, where the nonlinear operator F satisfies the φ‐Lipschitz condition and φ belongs to some admissible spaces. We further prove the existence of an invariant stable manifold around the μ‐pseudo almost automorphic solution
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Multiple peak solutions for polyharmonic equation with critical growth Math. Nachr. (IF 0.91) Pub Date : 2020-11-12 Yuxia Guo; Ting Liu
This paper is concerned with the following elliptic problem: ( − Δ ) m u = u + m ∗ − 1 + λ u − s 1 φ 1 , in B 1 , u ∈ D 0 m , 2 ( B 1 ) , ( P ) (P)where ( − Δ ) m is the polyharmonic operator, m ∗ = 2 N N − 2 m is the critical Sobolev embedding exponent. B1 is the unit ball in R N , s1 and λ > 0 are parameters, φ 1 > 0 is the eigenfunction of ( − Δ ) m , D 0 m , 2 ( B 1 ) corresponding to the first
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A topological approach to nonlocal elliptic partial differential equations on an annulus Math. Nachr. (IF 0.91) Pub Date : 2020-11-05 Christopher S. Goodrich
For q ≥ 1 we consider the nonlocal ordinary differential equation − a ∫ 0 1 | y | q d s y ′ ′ ( t ) = λ f ( t , y ( t ) ) , 0 < t < 1 , subject to the Dirichlet boundary conditions y ( 0 ) = 0 = y ( 1 ) . Due to the term a ∫ 0 1 | y | q ds appearing in the equation, this is a class of nonlocal differential equations. By using a novel order cone we are able to establish existence of a positive solution
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On a transmission problem for equation and dynamic boundary condition of Cahn–Hilliard type with nonsmooth potentials Math. Nachr. (IF 0.91) Pub Date : 2020-08-31 Pierluigi Colli; Takeshi Fukao; Hao Wu
This paper is concerned with well‐posedness of the Cahn–Hilliard equation subject to a class of new dynamic boundary conditions. The system was recently derived in Liu–Wu (Arch. Ration. Mech. Anal. 233 (2019), 167–247) via an energetic variational approach and it naturally fulfils three physical constraints such as mass conservation, energy dissipation and force balance. The target problem examined
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Higher differentiability for solutions of stationary p‐Stokes systems Math. Nachr. (IF 0.91) Pub Date : 2020-08-31 Flavia Giannetti; Antonia Passarelli di Napoli; Christoph Scheven
We consider weak solutions ( u , π ) : Ω → R n × R to stationary p‐Stokes systems of the type − div a ( x , E u ) + ∇ π + [ D u ] u = f , div u = 0 in Ω ⊂ R n , where the function a ( x , ξ ) satisfies p‐growth conditions in ξ and depends Hölder continuously on x. By E u we denote the symmetric part of the gradient D u and we write [ D u ] u for the convective term. In this setting, we establish results
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Sectorial extensions for ultraholomorphic classes defined by weight functions Math. Nachr. (IF 0.91) Pub Date : 2020-08-26 J. Jiménez‐Garrido; J. Sanz; Gerhard Schindl
We prove an extension theorem for ultraholomorphic classes defined by so‐called Braun–Meise–Taylor weight functions ω and transfer the proofs from the single weight sequence case from V. Thilliez to the weight function setting. We are following a different approach than the results obtained in a recent paper by the authors, more precisely we are working with real methods by applying the ultradifferentiable
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Pullbacks of universal Brill–Noether classes via Abel–Jacobi morphisms Math. Nachr. (IF 0.91) Pub Date : 2020-09-09 Nicola Pagani; Andrea T. Ricolfi; Jason van Zelm
Following Mumford and Chiodo, we compute the Chern character of the derived pushforward ch ( R • π * O ( D ) ) , for D an arbitrary element of the Picard group of the universal curve over the moduli stack of stable marked curves. This allows us to express the pullback of universal Brill–Noether classes via Abel–Jacobi sections to the compactified universal Jacobians, for all compactifications such
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Dual characterization of fractional capacity via solution of fractional p‐Laplace equation Math. Nachr. (IF 0.91) Pub Date : 2020-08-31 Shaoguang Shi; Lei Zhang
In terms of weak solutions of the fractional p‐Laplace equation with measure data, this paper offers a dual characterization for the fractional Sobolev capacity on bounded domain. In addition, two further results are given: one is an equivalent estimate for the fractional Sobolev capacity; the other is the removability of sets of zero capacity and its relation to solutions of the fractional p‐Laplace
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A probabilistic approach to a non‐local quadratic form and its connection to the Neumann boundary condition problem Math. Nachr. (IF 0.91) Pub Date : 2020-10-27 Zoran Vondraček
In this paper we look at a probabilistic approach to a non‐local quadratic form that has lately attracted some interest. This form is related to a recently introduced non‐local normal derivative. The goal is to construct two Markov processes: one corresponding to that form and the other which is related to a probabilistic interpretation of the Neumann problem. We also study the Dirichlet‐to‐Neumann
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Artificial boundary conditions for linearized stationary incompressible viscous flow around rotating and translating body Math. Nachr. (IF 0.91) Pub Date : 2020-10-22 P. Deuring; S. Kračmar; Š. Nečasová
We consider the linearized and nonlinear stationary incompressible flow around rotating and translating body in the exterior domain R 3 ∖ D ¯ , where D ⊂ R 3 is open and bounded, with Lipschitz boundary. We derive the pointwise estimates for the pressure in both cases. Moreover, we consider the linearized problem in a truncation domain D R : = B R ∖ D ¯ of the exterior domain R 3 ∖ D ¯ under certain
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Essentially finite generation of valuation rings in terms of classical invariants Math. Nachr. (IF 0.91) Pub Date : 2020-10-14 Steven Dale Cutkosky; Josnei Novacoski
The main goal of this paper is to study some properties of an extension of valuations from classical invariants. More specifically, we consider a valued field ( K , ν ) and an extension ω of ν to a finite extension L of K. Then we study when the valuation ring of ω is essentially finitely generated over the valuation ring of ν. We present a necessary condition in terms of classic invariants of the
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Well‐posedness of degenerate fractional integro‐differential equations in vector‐valued functional spaces Math. Nachr. (IF 0.91) Pub Date : 2020-07-30 Shangquan Bu; Gang Cai
We study the well‐posedness of the fractional degenerate integro‐differential equations ( P α ) : D α ( M u ) ( t ) = A u ( t ) + ∫ − ∞ t a ( t − s ) A u ( s ) d s + ∫ − ∞ t b ( t − s ) B u ( s ) d s + f ( t ) , ( t ∈ T : = [ 0 , 2 π ] ) , in Lebesgue–Bochner spaces L p ( T ; X ) and Besov spaces B p , q s ( T ; X ) , where A, B and M are closed linear operators on a Banach space X satisfying D ( A
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Multiplicity of solutions for fractional equation involving the Bessel operator in RN Math. Nachr. (IF 0.91) Pub Date : 2020-08-05 Nguyen Van Thin
The aim of this paper is to study the existence of solution to an equation involving the Bessel operator in R N ( I − Δ ) α u + λ V ( x ) u = γ f ( x , u ) , where λ , γ are real positive parameters, V : R N → R + is a continuous function, 0 < α < 1 with 2 α < N , f is a continuous function on R N × R which does not satisfy the Ambrosetti–Rabinowitz condition. By using the Fountain theorem and Morse
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The calculation of the sum of the spaces of the K‐method of real interpolation Math. Nachr. (IF 0.91) Pub Date : 2020-10-07 Evgenii I. Berezhnoĭ
It is shown that the calculation of the sum of the spaces of the K‐Peetre interpolation method can be reduced to the calculation of the sum of the cones of the concave functions included by the parameter in the definition of the spaces of the K‐Peetre interpolation method. As an example, a new extrapolation theorem for operators in Lipschitz spaces is obtained.
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Geometric regularity estimates for fully nonlinear elliptic equations with free boundaries Math. Nachr. (IF 0.91) Pub Date : 2020-10-05 João Vitor da Silva; Raimundo Alves Leitão Júnior; Gleydson Chaves Ricarte
In this manuscript we study geometric regularity estimates for problems driven by fully nonlinear elliptic operators (which can be either degenerate or singular when “the gradient is small”) under strong absorption conditions of the general form: G ( x , D u , D 2 u ) = f ( u ) χ { u > 0 } in Ω , where the mapping u ↦ f ( u ) fails to decrease fast enough at the origin, so allowing that nonnegative
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Direct limits of regular Lie groups Math. Nachr. (IF 0.91) Pub Date : 2020-10-03 Helge Glöckner
Let G be a regular Lie group which is a directed union of regular Lie groups G i (all modelled on possibly infinite‐dimensional, locally convex spaces). We show that G = lim ⟶ G i as a regular Lie group if G admits a so‐called direct limit chart. Notably, this allows the regular Lie group Diff c ( M ) of compactly supported diffeomorphisms to be interpreted as a direct limit of the regular Lie groups
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Noncompact quasi‐Einstein manifolds conformal to a Euclidean space Math. Nachr. (IF 0.91) Pub Date : 2020-09-28 Ernani Ribeiro Jr; Keti Tenenblat
The goal of this article is to investigate nontrivial m‐quasi‐Einstein manifolds globally conformal to an n‐dimensional Euclidean space. By considering such manifolds, whose conformal factors and potential functions are invariant under the action of an ( n − 1 ) ‐dimensional translation group, we provide a complete classification when λ = 0 and m ≥ 1 or m = 2 − n .
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Ricci η‐recurrent real hypersurfaces in 2‐dimensional nonflat complex space forms Math. Nachr. (IF 0.91) Pub Date : 2020-09-28 Yaning Wang
Let M be a Hopf hypersurface in a nonflat complex space form M 2 ( c ) , c ≠ 0 , of complex dimension two. In this paper, we prove that M has η‐recurrent Ricci operator if and only if it is locally congruent to a homogeneous real hypersurface of type (A) or (B) or a non‐homogeneous real hypersurface with vanishing Hopf principal curvature. This is an extension of main results in [17, 21] for real hypersurfaces
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Focusing nonlinear Hartree equation with inverse‐square potential Math. Nachr. (IF 0.91) Pub Date : 2020-09-21 Yu Chen; Jing Lu; Fanfei Meng
In this paper, we consider the scattering theory of the radial solution to focusing energy‐subcritical Hartree equation with inverse‐square potential in the energy space H 1 ( R d ) using the method from [4]. The main difficulties are due to the fact that the equation is not space‐translation invariant and that the nonlinearity is non‐local. Using the radial Sobolev embedding and a virial‐Morawetz
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Critical point equation and closed conformal vector fields Math. Nachr. (IF 0.91) Pub Date : 2020-09-21 J. F. da Silva Filho
In this article, we study the critical points of the total scalar curvature functional restricted to the space of metrics with constant scalar curvature of unitary volume, for simplicity, CPE metrics. Here, we prove that a CPE metric admitting a non‐trivial closed conformal vector field must be isometric to a round sphere metric, which provides a partial answer to the CPE conjecture.
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Remarks on solitons for inverse mean curvature flow Math. Nachr. (IF 0.91) Pub Date : 2020-09-21 Daehwan Kim; Juncheol Pyo
Homothetic and translating solitons for the inverse mean curvature flow (IMCF) in R n + 1 are self‐similar solutions deformed by only homothety and translation under IMCF, respectively. In this paper, we address some geometric properties of these solitons. To be specific, the incompleteness for the homothetic soliton of velocity C with 0 < C < 1 n and for any translating soliton are proved. In addition
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Finsler Hardy inequalities Math. Nachr. (IF 0.91) Pub Date : 2020-09-17 Anna Mercaldo; Megumi Sano; Futoshi Takahashi
In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a point or from the boundary of a domain. The sharpness and the non‐attainability of the constants in the inequalities are also proved.
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Stability of the radially symmetric stationary wave of the Burgers equation with multi‐dimensional initial perturbations in exterior domain Math. Nachr. (IF 0.91) Pub Date : 2020-09-15 Itsuko Hashimoto
The present paper is concerned with stability of the stationary solution of the Burgers equation in exterior domains in R n . In the previous papers [5, 6, 7] the asymptotic behavior of radially symmetric solutions for the multi‐dimensional Burgers equation in exterior domains in R n , n ≥ 3 , has been considered. The results [5, 6, 7] are restricted to stability of radially solutions within the class
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Littlewood–Paley–Stein operators on Damek–Ricci spaces Math. Nachr. (IF 0.91) Pub Date : 2020-09-11 Anestis Fotiadis; Effie Papageorgiou
We obtain pointwise upper bounds on the derivatives of the heat kernel on Damek–Ricci spaces and we study the L p ‐boundedness of Littlewood–Paley–Stein operators.
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Holomorphic symmetric differentials and a birational characterization of abelian varieties Math. Nachr. (IF 0.91) Pub Date : 2020-08-20 Ernesto C. Mistretta
A generically generated vector bundle on a smooth projective variety yields a rational map to a Grassmannian, called Kodaira map. We answer a previous question, raised by the asymptotic behaviour of such maps, giving rise to a birational characterization of abelian varieties. In particular we prove that, under the conjectures of the Minimal Model Program, a smooth projective variety is birational to
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Compactness and dichotomy in nonlocal shape optimization Math. Nachr. (IF 0.91) Pub Date : 2020-08-17 E. Parini; A. Salort
We prove a general result about the behaviour of minimizing sequences for nonlocal shape functionals satisfying suitable structural assumptions. Typical examples include functions of the eigenvalues of the fractional Laplacian under homogeneous Dirichlet boundary conditions. Exploiting a nonlocal version of Lions' concentration‐compactness principle, we prove that either an optimal shape exists or
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Hardy spaces for the Dunkl harmonic oscillator Math. Nachr. (IF 0.91) Pub Date : 2020-08-09 Agnieszka Hejna
Let Δ and L = Δ − ∥ x ∥ 2 be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space H 1 associated with the Dunkl harmonic oscillator by means of the nontangential maximal function with respect to the semigroup e t L . We prove that the space H 1 admits characterizations by relevant Riesz transforms and atomic decompositions. The atoms which occur in the atomic
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Aluthge transforms of unbounded weighted composition operators in L2‐spaces Math. Nachr. (IF 0.91) Pub Date : 2020-07-26 Chafiq Benhida; Piotr Budzyński; Jacek Trepkowski
We describe the Aluthge transform of an unbounded weighted composition operator acting in an L2‐space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate its dense definiteness. We characterize p‐hyponormality of unbounded weighted composition operators and provide results on how it is affected by the Aluthge transformation
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Improvements on Sawyer type estimates for generalized maximal functions Math. Nachr. (IF 0.91) Pub Date : 2020-07-23 Fabio Berra; Marilina Carena; Gladis Pradolini
In this paper we prove mixed inequalities for the maximal operator M Φ , for general Young functions Φ with certain additional properties, improving and generalizing some previous estimates for the Hardy–Littlewood maximal operator proved by E. Sawyer. We show that given r ≥ 1 , if u , v r are weights belonging to the A1‐Muckenhoupt class and Φ is a Young function as above, then the inequality u v
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Entropy for semigroup actions on general topological spaces Math. Nachr. (IF 0.91) Pub Date : 2020-07-23 Josiney A. Souza; Alexandre J. Santana
This paper introduces both notions of topological entropy and invariance entropy for semigroup actions on general topological spaces. We use the concept of admissible family of open coverings to extending and studying the notions of Adler–Konheim–McAndrew topological entropy, Bowen topological entropy, and invariance entropy to the general theory of topological dynamics.
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A note on the polynomial decay of a weakly dissipative viscoelastic system Math. Nachr. (IF 0.91) Pub Date : 2020-07-16 Jamilu Hashim Hassan; Salim A. Messaoudi
In this note we study an abstract class of weakly dissipative second‐order systems with finite memory. We establish the polynomial decay of Rivera, Naso and Vegni for the solution of the system under a very weak condition on the relaxation function.
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Littlewood–Paley characterization of BMO and Triebel–Lizorkin spaces Math. Nachr. (IF 0.91) Pub Date : 2020-07-15 Anton Tselishchev; Ioann Vasilyev
We prove a generalization of the Littlewood–Paley characterisation of the BMO space where the shifts of a Schwartz function are replaced by a family of functions with suitable conditions imposed on them. We also prove that a certain family of Triebel–Lizorkin spaces can be characterized in a similar way.
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Triangular representations of functions of operators with Schatten–von Neumann Hermitian components Math. Nachr. (IF 0.91) Pub Date : 2020-07-13 Michael Gil'
Let H be a separable Hilbert space with the unit operator I, let A be a bounded linear operator in H with a Schatten–von Neumann Hermitian component ( A − A ∗ ) / 2 i ( A ∗ means the operator adjoint to A) and let f ( z ) be a function analytic on the spectra of A and A ∗ . For f ( A ) we obtain the representation in the form of the sum of a normal operator and a quasi‐nilpotent Schatten–von Neumann
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Fractional Cauchy problem with memory effects Math. Nachr. (IF 0.91) Pub Date : 2020-07-13 Luciano Abadias; Edgardo Alvarez
We give an original representation integral formula for the resolvent families associated to the fractional Cauchy equation with memory effects C D t α u ( t ) − A u ( t ) + ∫ 0 t β ( t − s ) A u ( s ) d s = f ( t , u ( t ) ) , t ∈ [ 0 , T ] , T > 0 , where u ( 0 ) = u 0 ∈ X and A is a sectorial operator on a Banach space X. Moreover, we get spatial bounds for the resolvent families in order to study
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g‐natural symmetries on tangent bundles Math. Nachr. (IF 0.91) Pub Date : 2020-07-08 Mohamed Tahar Kadaoui Abbassi; Noura Amri; Giovanni Calvaruso
The study of symmetries is a well known research topic in differential geometry with relevant physical interpretations. Given a Riemannian manifold ( M , g ) , we consider pseudo‐Riemannian g‐natural metrics G on its tangent bundle T M and characterize conformal, homothetic and Killing vector fields of ( T M , G ) obtained from natural lifts of vector fields of M.
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Graphs encoding the generating properties of a finite group Math. Nachr. (IF 0.91) Pub Date : 2020-07-08 Cristina Acciarri, Andrea Lucchini
Assume that G is a finite group. For every a , b ∈ N , we define a graph Γ a , b ( G ) whose vertices correspond to the elements of G a ∪ G b and in which two tuples ( x 1 , ⋯ , x a ) and ( y 1 , ⋯ , y b ) are adjacent if and only if ⟨ x 1 , ⋯ , x a , y 1 , ⋯ , y b ⟩ = G . We study several properties of these graphs (isolated vertices, loops, connectivity, diameter of the connected components) and
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The asymptotic behavior for anisotropic parabolic p‐Laplacian equations Math. Nachr. (IF 0.91) Pub Date : 2020-07-07 Chenyin Qian; Daorui Yuan
The global existence and asymptotic behavior for anisotropic parabolic equation in R n are considered. By using the classical Galerkin approximation and suitable conditions on the weighted function, it is obtained the global estimate and the uniformly estimates for the global weak solution. Besides, the L 2 ( R n ) ∩ L r ( R n ) global attractor for anisotropic parabolic p‐Laplacian equation is also
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Depth and extremal Betti number of binomial edge ideals Math. Nachr. (IF 0.91) Pub Date : 2020-07-07 Arvind Kumar, Rajib Sarkar
Let G be a simple graph on the vertex set [n] and let J G be the corresponding binomial edge ideal. Let G = v ∗ H be the cone of v on H. In this article, we compute all the Betti numbers of J G in terms of the Betti numbers of J H and as a consequence, we get the Betti diagram of wheel graph. Also, we study Cohen–Macaulay defect of S / J G in terms of Cohen–Macaulay defect of S H / J H and using this
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A simpler description of the κ‐topologies on the spaces DLp,Lp,M1 Math. Nachr. (IF 0.91) Pub Date : 2020-07-06 Christian Bargetz, Eduard A. Nigsch, Norbert Ortner
For the spaces D L p , L p and M 1 , we consider the topology of uniform convergence on absolutely convex compact subsets of their (pre‐)dual space. Following the notation of J. Horváth's book we call these topologies κ‐topologies. They are given by a neighbourhood basis consisting of polars of absolutely convex and compact subsets of their (pre‐)dual spaces. In many cases it is more convenient to
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