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  • Inverse spectral results for non-abelian group actions
    Indag. Math. (IF 0.846) Pub Date : 2020-05-28
    Victor Guillemin; Zuoqin Wang

    In this paper we will extend to non-abelian groups inverse spectral results, proved by us in an earlier paper (Guillemin and Wang, 2016), for compact abelian groups, i.e. tori. More precisely, Let G be a compact Lie group acting isometrically on a compact Riemannian manifold X. We will show that for the Schrödinger operator −ħ2Δ+V with V∈C∞(X)G, the potential function V is, in some interesting examples

    更新日期:2020-05-28
  • Arithmetic on self-similar sets
    Indag. Math. (IF 0.846) Pub Date : 2020-05-22
    Bing Zhao; Xiaomin Ren; Jiali Zhu; Kan Jiang

    Let K1 and K2 be two one-dimensional homogeneous self-similar sets with the same ratio of contractions. Let f be a continuous function defined on an open set U⊂R2. Denote the continuous image of f by fU(K1,K2)={f(x,y):(x,y)∈(K1×K2)∩U}.In this paper we give a sufficient condition which guarantees that fU(K1,K2) contains some interiors. Our result is different from Simon and Taylor’s Simon and Taylor

    更新日期:2020-05-22
  • Diameter two properties and the Radon-Nikodým property in Orlicz spaces
    Indag. Math. (IF 0.846) Pub Date : 2020-05-16
    Anna Kamińska; Han Ju Lee; Hyung Joon Tag

    Some necessary and sufficient conditions are found for Banach function lattices to have the Radon-Nikodým property. Consequently it is shown that an Orlicz function space Lφ over a non-atomic σ-finite measure space (Ω,Σ,μ), not necessarily separable, has the Radon-Nikodým property if and only if φ is an N-function at infinity and satisfies the appropriate Δ2 condition. For an Orlicz sequence space

    更新日期:2020-05-16
  • Recent advances in the monodromy theory of integrable Hamiltonian systems
    Indag. Math. (IF 0.846) Pub Date : 2020-05-07
    N. Martynchuk; H.W. Broer; K. Efstathiou

    The notion of monodromy was introduced by J.J. Duistermaat as the first obstruction to the existence of global action coordinates in integrable Hamiltonian systems. This invariant was extensively studied since then and was shown to be non-trivial in various concrete examples of finite-dimensional integrable systems. The goal of the present paper is to give a brief overview of monodromy and discuss

    更新日期:2020-05-07
  • Nilpotent orbits of height 2 and involutions in the affine Weyl group
    Indag. Math. (IF 0.846) Pub Date : 2020-05-06
    Jacopo Gandini; Pierluigi Möseneder Frajria; Paolo Papi

    Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B⊂G be a Borel subgroup. Then B acts with finitely many orbits on the variety N2⊂g of the nilpotent elements whose height is at most 2. We provide a parametrization of the B-orbits in N2 in terms of subsets of pairwise orthogonal roots, and we provide a complete description

    更新日期:2020-05-06
  • Symplectic invariants of semitoric systems and the inverse problem for quantum systems
    Indag. Math. (IF 0.846) Pub Date : 2020-04-29
    Álvaro Pelayo

    Simple semitoric systems were classified about ten years ago in terms of a collection of invariants, essentially given by a convex polygon with some marked points corresponding to focus-focus singularities. Each marked point is endowed with labels which are symplectic invariants of the system. We will review the construction of these invariants, and explain how they have been generalized or applied

    更新日期:2020-04-29
  • Invariant generalized complex structures on partial flag manifolds
    Indag. Math. (IF 0.846) Pub Date : 2020-04-25
    Carlos A.B. Varea

    The aim of this paper is to classify all invariant generalized complex structures on a partial flag manifold FΘ with at most four isotropy summands. To classify them all we proved that an invariant generalized almost complex structure on FΘ is ‘constant’ in each component of the isotropy representation.

    更新日期:2020-04-25
  • Linear relations of Ohno sums of multiple zeta values
    Indag. Math. (IF 0.846) Pub Date : 2020-04-22
    Minoru Hirose; Hideki Murahara; Tomokazu Onozuka; Nobuo Sato

    Ohno’s relation is a well-known family of relations among multiple zeta values, which can naturally be regarded as a type of duality for a certain power series which we call an Ohno sum. In this paper, we investigate Q-linear relations among Ohno sums which are not contained in Ohno’s relation. We prove two new families of such relations, and pose several further conjectural families of such relations

    更新日期:2020-04-22
  • A new approach for the univalence of certain integral of harmonic mappings
    Indag. Math. (IF 0.846) Pub Date : 2020-04-18
    Hugo Arbeláez; Victor Bravo; Rodrigo Hernández; Willy Sierra; Osvaldo Venegas

    The principal goal of this paper is to extend the classical problem of finding the values of α∈ℂ for which either fˆα(z)=∫0z(f(ζ)∕ζ)αdζ or fα(z)=∫0z(f′(ζ))αdζ are univalent, whenever f belongs to some subclasses of univalent mappings in D, to the case of harmonic mappings, by considering the shear construction introduced by Clunie and Sheil-Small in [4].

    更新日期:2020-04-18
  • Bound on the radial derivatives of the Zernike circle polynomials (disk polynomials)
    Indag. Math. (IF 0.846) Pub Date : 2020-04-17
    A.J.E.M. Janssen

    We sharpen the bound n2k on the maximum modulus of the kth radial derivative of the Zernike circle polynomials (disk polynomials) of degree n to n2(n2−12)⋅...⋅(n2−(k−1)2)∕2k(1∕2)k. This bound is obtained from a result of Koornwinder on the non-negativity of connection coefficients of the radial parts of the circle polynomials when expanded into a series of Chebyshev polynomials of the first kind. The

    更新日期:2020-04-17
  • Deformation theory of holomorphic Cartan geometries
    Indag. Math. (IF 0.846) Pub Date : 2020-04-07
    Indranil Biswas; Sorin Dumitrescu; Georg Schumacher

    We introduce the deformation theory of holomorphic Cartan geometries. The infinitesimal automorphisms, as well as the infinitesimal deformations, of holomorphic Cartan geometries are computed. We also prove the existence of a semi-universal deformation of a holomorphic Cartan geometry.

    更新日期:2020-04-07
  • Strong rational Diophantine D(q)-triples
    Indag. Math. (IF 0.846) Pub Date : 2020-04-02
    Andrej Dujella; Matteo Paganin; Mohammad Sadek

    We show that for infinitely many square-free integers q there exist infinitely many triples of rational numbers {a,b,c} such that a2+q, b2+q, c2+q, ab+q, ac+q and bc+q are squares of rational numbers.

    更新日期:2020-04-02
  • A summation method based on the Fourier series of periodic distributions and an example arising in the Casimir effect
    Indag. Math. (IF 0.846) Pub Date : 2020-03-31
    Amol Sasane

    A generalised summation method is considered based on the Fourier series of periodic distributions. It is shown that eit−2e2it+3e3it−4e4it+−⋯=Pfeit(1+eit)2+iπ∑n∈Zδ(2n+1)π′, where Pfeit(1+eit)2∈D′(R) is the 2π-periodic distribution given by Pfeit(1+eit)2,φ=limϵ↘0∫(−δ,π−ϵ)∪(π+ϵ,2π+δ)φ(t)eit(1+eit)2dt−φ(π)tan(ϵ∕2) for φ∈D(R) with support supp(φ)⊂(−δ,2π+δ), where δ∈(0,π). Applying the generalised summation

    更新日期:2020-03-31
  • Representation of strongly truncated Riesz spaces
    Indag. Math. (IF 0.846) Pub Date : 2020-03-31
    Karim Boulabiar; Rawaa Hajji

    Following a recent idea by Ball, we introduce the notion of strongly truncated Riesz space with a suitable spectrum. We prove that, under an extra Archimedean type condition, any strongly truncated Riesz space is isomorphic to a uniformly dense Riesz subspace of a C0X-space. This turns out to be a direct generalization of the classical Kakutani Representation Theorem on Archimedean Riesz spaces with

    更新日期:2020-03-31
  • Non-extremal weight modules for quantized universal enveloping algebras
    Indag. Math. (IF 0.846) Pub Date : 2020-03-30
    Erik Koelink; Henrique Tyrrell

    For quantized universal enveloping algebras we construct weight modules by inducing representations of the centralizer of the Cartan subalgebra in the quantized universal enveloping algebra. The induced modules arising from finite-dimensional weight modules the centralizer algebra are studied. In particular, we study the induction of one-dimensional modules, and this is related to the study of commutative

    更新日期:2020-03-30
  • Norm Hilbert spaces over G-modules with a convex base
    Indag. Math. (IF 0.846) Pub Date : 2020-03-19
    E. Olivos; H. Ochsenius

    By analogy with the classical definition, a Norm Hilbert space E is defined as a Banach space over a valued field K in which each closed subspace has an orthocomplement. In the rank one case (that is, the value group as well as the set of norms of the space are contained in [0,∞)), they were described by van Rooij in his classical book of 1978, but the name itself was introduced in 1999 by Ochsenius

    更新日期:2020-03-19
  • Rate of approximation of zf′(z) by special sums associated with the zeros of the Bessel polynomials
    Indag. Math. (IF 0.846) Pub Date : 2020-03-12
    Mikhail A. Komarov

    Let αn1,…,αnn be the zeros of the nth Bessel polynomial yn(z) and let ank=1−αnk∕2, bnk=1+αnk∕2 (k=1,…,n). We propose the new formula zf′(z)≈∑k=1n(f(ankz)−f(bnkz))for numerical differentiation of analytic functions f(z)=∑0∞fmzm. This formula is exact for all polynomials of degree at most 2n. We find the sharp order of nonlocal estimate of the corresponding remainder for the case when all |fm|≤1. The

    更新日期:2020-03-12
  • Two bifurcation sets arising from the beta transformation with a hole at 0
    Indag. Math. (IF 0.846) Pub Date : 2020-03-07
    Simon Baker; Derong Kong

    Given β∈(1,2], the β-transformation Tβ:x↦βx(mod1) on the circle [0,1) with a hole [0,t) was investigated by Kalle et al. (2019). They described the set-valued bifurcation set Eβ≔{t∈[0,1):Kβ(t′)≠Kβ(t)∀t′>t},where Kβ(t)≔{x∈[0,1):Tβn(x)≥t∀n≥0} is the survivor set. In this paper we investigate the dimension bifurcation set ℬβ≔{t∈[0,1):dimHKβ(t′)≠dimHKβ(t)∀t′>t},where dimH denotes the Hausdorff dimension

    更新日期:2020-03-07
  • Sobolev embeddings with weights in complete Riemannian manifolds
    Indag. Math. (IF 0.846) Pub Date : 2020-03-03
    Eric Amar

    We prove Sobolev embedding Theorems with weights for vector bundles in a complete Riemannian manifold. We also get general Gaffney’s inequality with weights. As a consequence, under a “weak bounded geometry” hypothesis, we improve classical Sobolev embedding Theorems for vector bundles in a complete Riemannian manifold. We also improve known results on Gaffney’s inequality in a complete Riemannian

    更新日期:2020-03-03
  • Some martingales associated with multivariate Jacobi processes and Aomoto’s Selberg integral
    Indag. Math. (IF 0.846) Pub Date : 2020-02-27
    Michael Voit

    We study β-Jacobi diffusion processes on alcoves in RN, depending on 3 parameters. Using elementary symmetric functions, we present space–time-harmonic functions and martingales for these processes (Xt)t≥0 which are independent from one parameter. This leads to a formula for E(∏i=1N(y−Xt,i)) in terms of classical Jacobi polynomials. For t→∞ this yields a corresponding formula for Jacobi ensembles and

    更新日期:2020-02-27
  • Unions of cubes in Rn, combinatorics in Zn and the John–Nirenberg and John–Strömberg inequalities
    Indag. Math. (IF 0.846) Pub Date : 2020-02-25
    Michael Cwikel

    Suppose that the d-dimensional unit cube Q is the union of three disjoint “simple” sets E, F and G and that the volumes of E and F are both greater than half the volume of G. Does this imply that, for some cube W contained in Q. the volumes of E∩W and F∩W both exceed s times the volume of W for some absolute positive constant s? Here, by “simple” we mean a set which is a union of finitely many dyadic

    更新日期:2020-02-25
  • Logarithmic submajorization, uniform majorization and Hölder type inequalities for τ-measurable operators
    Indag. Math. (IF 0.846) Pub Date : 2020-02-24
    P.G. Dodds; T.K. Dodds; F.A. Sukochev; D. Zanin

    We extend the notion of the determinant function Λ, originally introduced by T.Fack for τ-compact operators, to a natural algebra of τ-measurable operators affiliated with a semifinite von Neumann algebra which coincides with that defined by Haagerup and Schultz in the finite case and on which the determinant function is shown to be submultiplicative. Application is given to Hölder type inequalities

    更新日期:2020-02-24
  • γ-Quantum product of white noise operators and applications
    Indag. Math. (IF 0.846) Pub Date : 2020-02-14
    Samah Horrigue

    The γ-quantum product of white noise operators which is the generalization of the γ-product, is introduced on the basis of the analytic characterization theorem for operator symbols established within the framework of white noise distribution theory. Existence and uniqueness of solutions are proved for a certain class of ordinary differential equations for Fock space operators.

    更新日期:2020-02-14
  • Valuations: From orthogonal additivity to orthosymmetry
    Indag. Math. (IF 0.846) Pub Date : 2020-02-14
    Gerard Buskes; Stephan Roberts

    We prove that polynomial valuations on vector lattices correspond to orthosymmetric multilinear maps. As a consequence we obtain a concise proof of the correspondence between orthosymmetry and orthogonal additivity.

    更新日期:2020-02-14
  • On the structure of variable exponent spaces
    Indag. Math. (IF 0.846) Pub Date : 2020-02-11
    Julio Flores; Francisco L. Hernández; César Ruiz; Mauro Sanchiz

    The first part of this paper surveys several results on the lattice structure of variable exponent Lebesgue function spaces (or Nakano spaces) Lp(⋅)(Ω). In the second part strictly singular and disjointly strictly singular operators between spaces Lp(⋅)(Ω) are studied. New results on the disjoint strict singularity of the inclusions Lp(⋅)(Ω)↪Lq(⋅)(Ω) are given.

    更新日期:2020-02-11
  • An intuitive approach to the Martin boundary
    Indag. Math. (IF 0.846) Pub Date : 2020-02-01
    Peter A. Loeb

    An intuitive probabilistic alternative for the construction of the Martin boundary is presented along with a construction of maximal representing measures for positive harmonic functions.

    更新日期:2020-02-01
  • Validated computations for connecting orbits in polynomial vector fields
    Indag. Math. (IF 0.846) Pub Date : 2020-01-31
    Jan Bouwe van den Berg; Ray Sheombarsing

    In this paper we present a computer-assisted procedure for proving the existence of transverse heteroclinic orbits connecting hyperbolic equilibria of polynomial vector fields. The idea is to compute high-order Taylor approximations of local charts on the (un)stable manifolds by using the Parameterization Method and to use Chebyshev series to parameterize the orbit in between, which solves a boundary

    更新日期:2020-01-31
  • The Grothendieck property in Marcinkiewicz spaces
    Indag. Math. (IF 0.846) Pub Date : 2020-01-30
    B. de Pagter; F.A. Sukochev

    The main purpose of this paper is to fully characterize continuous concave functions ψ such that the corresponding Marcinkiewicz Banach function space Mψ is a Grothendieck space.

    更新日期:2020-01-30
  • Optimal extension of the Fourier transform and convolution operator on compact groups
    Indag. Math. (IF 0.846) Pub Date : 2020-01-27
    Manoj Kumar; N. Shravan Kumar

    Let G be a compact group (not necessarily abelian) and let Φ be a Young function satisfying the Δ2-condition. We determine the optimal domain and the associated extended operator for both Fourier transform and the convolution operator defined on the Orlicz spaces LΦ(G).

    更新日期:2020-01-27
  • Bivariate functions of bounded variation: Fractal dimension and fractional integral
    Indag. Math. (IF 0.846) Pub Date : 2020-01-27
    S. Verma; P. Viswanathan

    In contrast to the univariate case, several definitions are available for the notion of bounded variation for a bivariate function. This article is an attempt to study the Hausdorff dimension and box dimension of the graph of a continuous function defined on a rectangular region in R2, which is of bounded variation according to some of these approaches. We show also that the Riemann–Liouville fractional

    更新日期:2020-01-27
  • On existence and uniqueness of solution for a hydrodynamic problem related to water artificial circulation in a lake
    Indag. Math. (IF 0.846) Pub Date : 2020-01-25
    Francisco J. Fernández; Lino J. Alvarez-Vázquez; Aurea Martínez

    In this work we introduce a well-posed mathematical model for the processes involved in the artificial circulation of water, in order to avoid eutrophication phenomena, for instance, in a lake. This novel and general formulation is based on the modified Navier–Stokes equations following the Smagorinsky model of turbulence, and presenting a suitable nonhomogeneous Dirichlet boundary condition. For the

    更新日期:2020-01-25
  • Hausdorff–Young inequality for Orlicz spaces on compact homogeneous manifolds
    Indag. Math. (IF 0.846) Pub Date : 2020-01-25
    Vishvesh Kumar; Michael Ruzhansky

    We prove the classical Hausdorff–Young inequality for Orlicz spaces on compact homogeneous manifolds.

    更新日期:2020-01-25
  • m-accretive Laplacian on a non symmetric graph
    Indag. Math. (IF 0.846) Pub Date : 2020-01-25
    Colette Anné; Marwa Balti; Nabila Torki-Hamza

    We consider a non self-adjoint Laplacian on a directed graph with non-symmetric weights on edges. We give a criterion for the m-accretiveness and the m-sectoriality of this Laplacian. Our results are based on a comparison of this operator with its symmetric part for which we can apply different results concerning essential self-adjointness of a symmetric Laplace operator on an infinite graph. This

    更新日期:2020-01-25
  • On another extension of coherent pairs of measures
    Indag. Math. (IF 0.846) Pub Date : 2020-01-18
    K. Castillo; D. Mbouna

    Let M and N be fixed non-negative integer numbers and let πN be a polynomial of degree N. Suppose that (Pn)n≥0 and (Qn)n≥0 are two orthogonal polynomial sequences such that πN(x)Pn+m(m)(x)=∑j=n−Mn+Nrn,jQj+k(k)(x)(n=0,1,…),where rn,j are complex numbers independent of x. It is shown that under natural constraints, (Pn)n≥0 and (Qn)n≥0 are semiclassical orthogonal polynomial sequences. Moreover, their

    更新日期:2020-01-18
  • Densities of generalized stochastic areas and windings arising from Anti-de Sitter and Hopf fibrations
    Indag. Math. (IF 0.846) Pub Date : 2019-12-23
    Nizar Demni

    In the first part of this paper, we derive explicit expressions of the semi-group densities of generalized stochastic areas arising from the Anti-de Sitter and the Hopf fibrations. Motivated by the number-theoretical connection between the Heisenberg group and Dirichlet series, we express the Mellin transform of the generalized stochastic area corresponding to the one-dimensional Anti de Sitter fibration

    更新日期:2019-12-23
  • Diffeomorphisms preserving Morse–Bott functions
    Indag. Math. (IF 0.846) Pub Date : 2019-12-16
    Olexandra Khohliyk; Sergiy Maksymenko

    Let f:M→R be a Morse–Bott function on a closed manifold M, so the set Σf of its critical points is a closed submanifold whose connected components may have distinct dimensions. Denote by S(f)={h∈D(M)∣f∘h=h} the group of diffeomorphisms of M preserving f and let D(Σf) be the group of diffeomorphisms of Σf. We prove that the “restriction to Σf” map ρ:S(f)→D(Σf), ρ(h)=h|Σf, is a locally trivial fibration

    更新日期:2019-12-16
  • Dilation invariant Banach limits
    Indag. Math. (IF 0.846) Pub Date : 2019-12-14
    E. Semenov; F. Sukochev; A. Usachev; D. Zanin

    We study two subclasses of Banach limits: that consisting of Banach limits which are invariant with respect of the Cesàro operator and that consisting of Banach limits which are invariant with respect to all dilations. We prove that the first is a proper subset of the second. We also show that these classes are at maximal distance from the set extB of all extreme points of the set of all Banach limits

    更新日期:2019-12-14
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