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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.

    更新日期:2020-09-18
  • 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

    更新日期:2020-09-15
  • 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.

    更新日期:2020-09-11
  • 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

    更新日期:2020-09-10
  • 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

    更新日期:2020-09-01
  • 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

    更新日期:2020-09-01
  • Ergodicity for neutral type SDEs with infinite length of memory
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-24
    Jianhai Bao; Feng‐Yu Wang; Chenggui Yuan

    In this paper, the weak Harris theorem developed in [18] is illustrated by using a straightforward Wasserstein coupling, which implies the exponential ergodicity of the functional solutions to a range of neutral type SDEs with infinite length of memory. A concrete example is presented to illustrate the main result.

    更新日期:2020-09-01
  • 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

    更新日期:2020-09-01
  • Weighted operator least squares problems and the J‐trace in Krein spaces
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-29
    Maximiliano Contino; Alejandra Maestripieri; Stefania Marcantognini

    Given B , C and W operators in the algebra L ( H ) of bounded linear operators on the Krein space H , the minimization problem min ( B X − C ) # W ( B X − C ) , for X ∈ L ( H ) , is studied when the weight W is selfadjoint. The analogous maximization and min‐max problems are also considered. Complete answers to these problems and to those naturally associated to trace clase operators on Krein spaces

    更新日期:2020-09-01
  • 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

    更新日期:2020-09-01
  • Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-06
    Wencai Liu

    For perturbed Stark operators H u = − u ′ ′ − x u + q u , the author has proved that lim sup x → ∞ x 1 2 | q ( x ) | must be larger than 1 2 N 1 2 in order to create N linearly independent eigensolutions in L 2 ( R + ) [29]. In this paper, we apply generalized Wigner–von Neumann type functions to construct embedded eigenvalues for a class of Schrödinger operators, including a proof that the bound 1

    更新日期:2020-09-01
  • Revisiting the Gross–Zagier discriminant formula
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-24
    Dongxi Ye

    We derive a formula for the discriminant of the ring class polynomial of conductor N associated to the j‐invariant and an imaginary quadratic field of odd discriminant − d using the theory of Borcherds lifts. When d is a prime and N = 1 , the formula recovers the Gross–Zagier discriminant formula.

    更新日期:2020-09-01
  • Multiple solutions for superlinear Klein–Gordon–Maxwell equations†
    Math. Nachr. (IF 0.91) Pub Date : 2020-07-02
    Dong‐Lun Wu; Hongxia Lin

    In this paper, we consider the following Klein–Gordon–Maxwell equations − Δ u + V ( x ) u − ( 2 ω + ϕ ) ϕ u = f ( x , u ) + h ( x ) in R 3 , − Δ ϕ + ϕ u 2 = − ω u 2 in R 3 , where ω > 0 is a constant, u, ϕ : R 3 → R , V : R 3 → R is a potential function. By assuming the coercive condition on V and some new superlinear conditions on f, we obtain two nontrivial solutions when h is nonzero and infinitely

    更新日期:2020-09-01
  • 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

    更新日期:2020-08-31
  • 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

    更新日期:2020-08-31
  • 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

    更新日期:2020-08-27
  • 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

    更新日期:2020-08-21
  • 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

    更新日期:2020-08-18
  • 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

    更新日期:2020-08-10
  • 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

    更新日期:2020-08-05
  • 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 (

    更新日期:2020-07-31
  • 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

    更新日期:2020-07-27
  • 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

    更新日期:2020-07-24
  • 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.

    更新日期:2020-07-24
  • A p‐adic analogue of Siegel's theorem on sums of squares
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-08
    Sylvy Anscombe; Philip Dittmann; Arno Fehm

    Siegel proved that every totally positive element of a number field K is the sum of four squares, so in particular the Pythagoras number is uniformly bounded across number fields. The p‐adic Kochen operator provides a p‐adic analogue of squaring, and a certain localisation of the ring generated by this operator consists of precisely the totally p‐integral elements of K . We use this to formulate and

    更新日期:2020-07-23
  • The differentiation operator in the space of uniformly convergent Dirichlet series
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-08
    José Bonet

    Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fréchet space of all Dirichlet series that are uniformly convergent in all half‐planes { s ∈ C | Re s > ε } for each ε > 0 . The properties of the formal inverse of the differentiation are also investigated.

    更新日期:2020-07-23
  • Besov regularity for solutions of elliptic equations with variable exponents
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-28
    Raffaella Giova

    We establish the higher fractional differentiability of the solutions of a problem in divergence form of the type div A ( x , D u ) = div | F | p ( x ) − 2 2 F in Ω , u = 0 on ∂ Ω . The main features consist in assuming that the partial map ξ → A ( x , ξ ) has p ( x ) ‐growth, the datum F is Besov regular and both the partial map x → A ( x , ξ ) and the function x → p ( x ) are Orlicz–Besov regular

    更新日期:2020-07-23
  • Radial solutions of semilinear elliptic equations with prescribed asymptotic behavior
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-19
    Hassan Ibrahim

    We consider semilinear elliptic equations of the form Δ u + g ( u ) = 0 on R N . Given a suitable positive root z of g , we discuss the existence of positive radial solutions u with u ( ∞ ) = z .

    更新日期:2020-07-23
  • Algebraicity of analytic maps to a hyperbolic variety
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-25
    Ariyan Javanpeykar; Robert Kucharczyk

    Let X be a complex algebraic variety. We say that X is Borel hyperbolic if, for every finite type reduced scheme S over the complex numbers, every holomorphic map from S to X is algebraic. We use a transcendental specialization technique to prove that X is Borel hyperbolic if and only if, for every smooth affine complex algebraic curve C , every holomorphic map from C to X is algebraic. We use the

    更新日期:2020-07-23
  • Average distribution of k‐free numbers in arithmetic progressions
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-25
    Kui Liu; Igor E. Shparlinski; Tianping Zhang

    We obtain a new bound on the average value of the error term in the asymptotic formula for the number of k‐free numbers in arithmetic progressions. In particular, we improve the results of J. Gibson (2014) and C. Hooley (1975).

    更新日期:2020-07-23
  • Coarse homotopy groups
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-14
    Paul D. Mitchener; Behnam Norouzizadeh; Thomas Schick

    In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse homotopy groups. The main result is that the coarse homotopy groups of a cone over a compact simplicial complex coincide with the usual homotopy groups of the underlying

    更新日期:2020-07-23
  • Null screen quasi‐conformal hypersurfaces in semi‐Riemannian manifolds and applications
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-08
    Matias Navarro; Oscar Palmas; Didier A. Solis

    We introduce a class of null hypersurfaces of a semi‐Riemannian manifold, namely, screen quasi‐conformal hypersurfaces, whose geometry may be studied through the geometry of its screen distribution. In particular, this notion allows us to extend some results of previous works to the case in which the sectional curvature of the ambient space is different from zero. As applications, we study umbilical

    更新日期:2020-07-23
  • Gaussian density estimates for solutions of fully coupled forward‐backward SDEs
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-25
    Christian Olivera; Evelina Shamarova

    We obtain upper and lower Gaussian density estimates for the laws of each component of the solution to a one‐dimensional fully coupled forward‐backward SDE. Our approach relies on the link between FBSDEs and quasilinear parabolic PDEs, and is fully based on the use of classical results on PDEs rather than on manipulation of FBSDEs, compared to other papers on this topic. This essentially simplifies

    更新日期:2020-07-23
  • Advection‐diffusion dynamics with nonlinear boundary flux as a model for crystal growth
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-15
    Antoine Pauthier; Arnd Scheel

    We analyze the effect of nonlinear boundary conditions on an advection‐diffusion equation on the half‐line. Our model is inspired by models for crystal growth where diffusion models diffusive relaxation of a displacement field, advection is induced by apical growth, and boundary conditions incorporate non‐adiabatic effects on displacement at the boundary. The equation, in particular the boundary fluxes

    更新日期:2020-07-23
  • On Bohr's theorem for general Dirichlet series
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-17
    I. Schoolmann

    We present quantitative versions of Bohr's theorem on general Dirichlet series D = ∑ a n e − λ n s assuming different assumptions on the frequency λ = ( λ n ) , including the conditions introduced by Bohr and Landau. Therefore, using the summation method by typical (first) means invented by M. Riesz, without any condition on λ, we give upper bounds for the norm of the partial sum operator S N ( D )

    更新日期:2020-07-23
  • On 4‐dimensional Lorentzian affine hypersurfaces with an almost symplectic form
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-25
    Michal Szancer; Zuzanna Szancer

    In this paper we study 4‐dimensional affine hypersurfaces with a Lorentzian second fundamental form additionally equipped with an almost symplectic structure ω. We prove that the rank of the shape operator is at most one if R k · ω = 0 or ∇ k ω = 0 for some positive integer k . This result is the final step in a classification of Lorentzian affine hypersurfaces with higher order parallel almost symplectic forms

    更新日期:2020-07-23
  • New results on common properties of the products AC and BA, II
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-04
    Qingping Zeng; Kai Yan; Shifang Zhang

    In this note, we continue to investigate common properties of the products in the setting of rings, bounded linear operators, or Banach algebras. We prove: (i) If a , b , c are elements in a unital associative ring R satisfying a b a = a c a , then von Neumann regularity (resp. generalized Fredholmness relative to an ideal I of R ) of 1 − a c is converted into that of 1 − b a . (ii) If A , B , C are

    更新日期:2020-07-23
  • 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.

    更新日期:2020-07-16
  • 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.

    更新日期:2020-07-16
  • 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

    更新日期:2020-07-13
  • 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

    更新日期:2020-07-13
  • 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 .

    更新日期:2020-07-08
  • 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

    更新日期:2020-07-07
  • On the classification and modular extendability of E0‐semigroups on factors
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-11
    Panchugopal Bikram; Daniel Markiewicz

    In this paper we study modular extendability and equimodularity of endomorphisms and E0‐semigroups on factors, when these definitions are recast to the context of faithful normal semifinite weights and this dependency is analyzed. We show that modular extendability is a property that does not depend on the choice of weights, it is a cocycle conjugacy invariant and it is preserved under tensoring. Furthermore

    更新日期:2020-06-26
  • Generating pairs of projective special linear groups that fail to lift
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-18
    Jan Boschheidgen; Benjamin Klopsch; Anitha Thillaisundaram

    The following problem was originally posed by B. H. Neumann and H. Neumann. Suppose that a group G can be generated by n elements and that H is a homomorphic image of G . Does there exist, for every generating n ‐tuple ( h 1 , … , h n ) of H , a homomorphism ϑ : G → H and a generating n ‐tuple ( g 1 , … , g n ) of G such that ( g 1 ϑ , … , g n ϑ ) = ( h 1 , … , h n ) ?

    更新日期:2020-06-26
  • Isometric immersions of space forms into Sp×R
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-25
    S. Canevari; Ruy Tojeiro

    In this article we classify isometric immersions f : M n ( c ) → S n + p × R of Riemannian manifolds of dimension n and constant sectional curvature c ≤ 1 into the product space S n + p × R , p ≤ n − 3 , where S m denotes the m ‐dimensional unit sphere.

    更新日期:2020-06-26
  • Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-19
    Volodymyr Derkach; Seppo Hassi; Mark Malamud

    With a closed symmetric operator A in a Hilbert space H a triple Π = { H , Γ 0 , Γ 1 } of a Hilbert space H and two abstract trace operators Γ0 and Γ1 from A ∗ to H is called a generalized boundary triple for A ∗ if an abstract analogue of the second Green's formula holds. Various classes of generalized boundary triples are introduced and corresponding Weyl functions M ( · ) are investigated. The most

    更新日期:2020-06-26
  • A fibered description of the vector‐valued spectrum
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-04
    Verónica Dimant; Joaquín Singer

    For Banach spaces X and Y we study the vector‐valued spectrum M ∞ ( B X , B Y ) , that is the set of non null algebra homomorphisms from H ∞ ( B X ) to H ∞ B Y , which is naturally projected onto the closed unit ball of H ∞ ( B Y , X ∗ ∗ ) . The aim of this article is to describe the fibers defined by this projection, searching for analytic balls and considering Gleason parts.

    更新日期:2020-06-26
  • A boundary Schwarz lemma for mappings from the unit polydisc to irreducible bounded symmetric domains
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-07
    Hidetaka Hamada; Gabriela Kohr

    In this paper, we obtain a boundary Schwarz lemma for C 1 (pluriharmonic, holomorphic) mappings from the unit polydisc U n in C n to irreducible bounded symmetric domains realized as the unit ball B X of an N ‐dimensional simple JB*‐triple X . In particular, we obtain a version of the boundary Schwarz lemma for C 1 (pluriharmonic, holomorphic) mappings from U n into the Euclidean unit ball B N in C

    更新日期:2020-06-26
  • BV‐packing integral in Rn
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-14
    Kristýna Kuncová

    We introduce new integrals (called packing R and R ∗ integrals) which combine advantages of integrals developed by Pfeffer [17], Malý [12], Kuncová and Malý [10] and Malý and Pfeffer [13]. We prove Gauss–Green theorem in generality of the new integrals and provide comparison with the integrals mentioned above and some others (like M C α by Ball and Preiss [2]).

    更新日期:2020-06-26
  • Classification and syzygies of smooth projective varieties with 2‐regular structure sheaf
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-19
    Sijong Kwak; Jinhyung Park

    The geometric and algebraic properties of smooth projective varieties with 1‐regular structure sheaf are well understood, and the complete classification of these varieties is a classical result. The aim of this paper is to study the next case: smooth projective varieties with 2‐regular structure sheaf. First, we give a classification of such varieties using adjunction mappings. Next, under suitable

    更新日期:2020-06-26
  • On Pólya–Szegö reverse of Schwarz's inequality
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-04
    Zdzisław Otachel

    We present some new results on the Cauchy–Schwarz inequality in inner product spaces, where four vectors are involved. This naturally extends Pólya–Szegö reverse of Schwarz's inequality onto complex inner product spaces. Applications to the famous Hadamard's inequality about determinants and the triangle inequality for norms are given.

    更新日期:2020-06-26
  • Sharp multi‐weighted bounds for multilinear fractional rough operators and Cohen–Gosselin type commutators
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-05
    Xiangxing Tao; Xiao Yu

    In the article, we consider the multilinear fraction maximal operators and the multilinear fraction integrals with rough kernels, we introduce a new class for ( m + 1 ) ‐weights tuple ( u , ω ⃗ ) , and prove the optimal constant estimates of the sharp multi‐weighted bounds for both operators. We also show the sharp multi‐weighted bounds for the Cohen–Gosselin type multi‐commutator of the both operators

    更新日期:2020-06-26
  • Nef‐partitions arising from unimodular configurations
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-22
    Hidefumi Ohsugi; Akiyoshi Tsuchiya

    Reflexive polytopes have been studied from viewpoints of combinatorics, commutative algebra and algebraic geometry. A nef‐partition of a reflexive polytope P is a decomposition P = P 1 + ⋯ + P r such that each P i is a lattice polytope containing the origin. Batyrev and van Straten gave a combinatorial method for explicit constructions of mirror pairs of Calabi–Yau complete intersections obtained from

    更新日期:2020-06-22
  • Erratum to the paper “Quadratic descent of hermitian forms”
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-22
    A.‐H. Nokhodkar

    There exists a mistake in the proof of Theorem 4.2. We present a new proof of this theorem, which shows that the main results of the paper are still true.

    更新日期:2020-06-22
  • Parallel and totally geodesic hypersurfaces of non‐reductive homogeneous four‐manifolds
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-21
    Giovanni Calvaruso; Reinier Storm; Joeri Van der Veken

    We classify totally geodesic and parallel hypersurfaces of four‐dimensional non‐reductive homogeneous pseudo‐Riemannian manifolds.

    更新日期:2020-06-21
  • A classification of surfaces with isotropic Para‐Blaschke tensor
    Math. Nachr. (IF 0.91) Pub Date : 2020-06-15
    Fengjiang Li; Jianbo Fang; Jianxiang Li

    Let M 2 → S 3 be an umbilic‐free surface. Four basic invariants of M2 under the Möbius transformation group of S 3 are the Möbius metric g, the Blaschke tensor A, the Möbius second fundamental form B and the Möbius form Φ. A symmetric (0,2) tensor D = A + μ B called Para‐Blaschke tensor, where μ is constant, is also Möbius invariant. In this paper, we classify the surfaces with isotropic Para‐Blaschke

    更新日期:2020-06-15
  • A Desch–Schappacher perturbation theorem for bi‐continuous semigroups
    Math. Nachr. (IF 0.91) Pub Date : 2020-05-04
    Christian Budde; Bálint Farkas

    We prove a Desch–Schappacher type perturbation theorem for one‐parameter semigroups on Banach spaces which are not strongly continuous for the norm, but possess a weaker continuity property. In this paper we chose to work in the framework of bi‐continuous semigroups. This choice has the advantage that we can treat in a unified manner two important classes of semigroups: implemented semigroups on the

    更新日期:2020-05-04
  • Lattice points in bodies of revolution II
    Math. Nachr. (IF 0.91) Pub Date : 2020-04-27
    Fernando Chamizo; Carlos Pastor

    In [3] it was shown that when a three‐dimensional smooth convex body has rotational symmetry around a coordinate axis one can find better bounds for the lattice point discrepancy than what is known for more general convex bodies. To accomplish this, however, it was necessary to assume a non‐vanishing condition on the third derivative of the generatrix. In this article we drop this condition, showing

    更新日期:2020-04-27
  • Liouville type theorems for Hardy–Hénon equations with concave nonlinearities
    Math. Nachr. (IF 0.91) Pub Date : 2020-04-22
    Wei Dai; Guolin Qin

    In this paper, we are concerned with the Hardy–Hénon equations − Δ u = | x | a u p and Δ 2 u = | x | a u p with a ∈ R and p ∈ ( 0 , 1 ] . Inspired by Serrin and Zou [25], we prove Liouville theorems for nonnegative solutions to the above Hardy–Hénon equations (Theorem 1.1 and Theorem 1.3), that is, the unique nonnegative solution is u ≡ 0 .

    更新日期:2020-04-22
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