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  • Algebraic topology of special Lagrangian manifolds
    Indag. Math. (IF 0.882) Pub Date : 2020-10-17
    Mustafa Kalafat; Eyüp Yalçınkaya

    In this paper, we prove various results on the topology of the Grassmannian of oriented 3-planes in Euclidean 6-space and compute its cohomology ring. We give self-contained proofs. These spaces come up when studying submanifolds of manifolds with calibrated geometries. We collect these results here for the sake of completeness. As applications of our algebraic topological study we present some results

    更新日期:2020-10-17
  • On a generalization of the cyclic sum formula for finite multiple zeta and zeta-star values
    Indag. Math. (IF 0.882) Pub Date : 2020-10-12
    Hideki Murahara

    The cyclic sum formulas for multiple zeta and zeta-star values were respectively proved by Hoffman and Ohno, and Ohno and Wakabayashi. Kawasaki and Oyama obtained an analogous formulas for finite multiple zeta and zeta-star values. In this paper, we give a generalization of Kawasaki and Oyama’s results.

    更新日期:2020-10-13
  • Strata of a disconnected reductive group
    Indag. Math. (IF 0.882) Pub Date : 2020-10-10
    G. Lusztig

    Let D be a fixed connected component of a reductive algebraic group over an algebraically closed field. We use a variant of the Springer representation to define and study a partition of D into finitely many Strata, one of which is the open set of regular elements. We show that the Strata of D are indexed by a set defined purely in terms of the Weyl group and its automorphism defined by D.

    更新日期:2020-10-11
  • Reductivity properties over an affine base
    Indag. Math. (IF 0.882) Pub Date : 2020-10-02
    Wilberd van der Kallen

    When the base ring is not a field, power reductivity of a group scheme is a basic notion, intimately tied with finite generation of subrings of invariants. Geometric reductivity is weaker and less pertinent in this context. We give a survey of these properties and their connections.

    更新日期:2020-10-02
  • On modular signs of half integral weights
    Indag. Math. (IF 0.882) Pub Date : 2020-10-02
    Bin Chen; Jie Wu; Yichao Zhang

    In this paper, we consider the first negative eigenvalue of eigenforms of half-integral weight k+1∕2 and obtain an almost type bound.

    更新日期:2020-10-02
  • Semisimple symmetric contact spaces
    Indag. Math. (IF 0.882) Pub Date : 2020-09-28
    Dmitri Alekseevsky; Claudio Gorodski

    We classify contact manifolds (M,D) which are homogeneous under a connected semisimple Lie group G, and symmetric in the sense that there exists a contactomorphism of (M,D) normalizing G, fixing a point o in M and restricting to minus identity along Do.

    更新日期:2020-09-28
  • Optimal estimates for hyperbolic Poisson integrals of functions in Lp with p>1 and radial eigenfunctions of the Hyperbolic Laplacian
    Indag. Math. (IF 0.882) Pub Date : 2020-09-22
    Jiaolong Chen; David Kalaj

    Assume that p∈(1,∞] and u=Ph[ϕ], where ϕ∈Lp(Sn−1,Rn). Then for any x∈Bn, we obtain the sharp inequalities |u(x)|≤Cq1q(x)(1−|x|2)n−1p‖ϕ‖Lpand|u(x)|≤Cq1q(1−|x|2)n−1p‖ϕ‖Lp for some function Cq(x) and constant Cq in terms of Gauss hypergeometric and Gamma functions, where q is the conjugate of p. This result generalizes and extends some known results from harmonic mapping theory (Kalaj and Marković (2012

    更新日期:2020-09-22
  • The functional calculus approach to the spectral theorem
    Indag. Math. (IF 0.882) Pub Date : 2020-09-19
    Markus Haase

    A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators, here the functional calculus is not treated as a subordinate but as the central concept. Based on five simple axioms for a “measurable functional calculus”, the theory

    更新日期:2020-09-20
  • The homotopy significant spectrum compared to the Krasnoselskii spectrum
    Indag. Math. (IF 0.882) Pub Date : 2020-09-18
    S.J. Fokma; J.W. Portegies

    How to generalize the concept of eigenvalues of quadratic forms to eigenvalues of arbitrary, even, homogeneous continuous functionals, if stability of the set of eigenvalues under small perturbations is required? We compare two possible generalizations, Gromov’s homotopy significant spectrum and the Krasnoselskii spectrum. We show that in the finite dimensional case, the Krasnoselskii spectrum is contained

    更新日期:2020-09-20
  • Cusps, congruence groups and Monstrous dessins
    Indag. Math. (IF 0.882) Pub Date : 2020-09-16
    Valdo Tatitscheff; Yang-Hui He; John McKay

    We study general properties of the dessins d’enfants associated with the Hecke congruence subgroups Γ0(N) of the modular group PSL2(Z). The definition of the Γ0(N) as the stabilisers of couples of projective lattices in a two-dimensional vector space gives an interpretation of the quotient set Γ0(N)∖PSL2(Z) as the projective lattices N-hyperdistant from a reference one, and hence as the projective

    更新日期:2020-09-16
  • Normal resonances in a double Hopf bifurcation
    Indag. Math. (IF 0.882) Pub Date : 2020-09-12
    Henk Broer; Heinz Hanßmann; Florian Wagener

    We introduce a framework to systematically investigate the resonant double Hopf bifurcation. We use the basic invariants of the ensuing T1–action to analyse the approximating normal form truncations in a unified manner. In this way we obtain a global description of the parameter space and thus find the organising resonance droplet, which is the present analogue of the resonant gap. The dynamics of

    更新日期:2020-09-12
  • Intersection of Siepinski gasket with its translation
    Indag. Math. (IF 0.882) Pub Date : 2020-09-10
    Yi Cai; Wenxia Li

    Let E be the Sierpinski gasket, i.e., the self-similar set generated by the IFS fa(x)=x+aq:a∈{(0,0),(0,1),(1,0)}. In this paper, we provide a description of the following set for 2

    更新日期:2020-09-10
  • Toeplitz band matrices with small random perturbations
    Indag. Math. (IF 0.882) Pub Date : 2020-09-10
    Johannes Sjöstrand; Martin Vogel

    We study the spectra of N×N Toeplitz band matrices perturbed by small complex Gaussian random matrices, in the regime N≫1. We prove a probabilistic Weyl law, which provides an precise asymptotic formula for the number of eigenvalues in certain domains, which may depend on N, with probability sub-exponentially (in N) close to 1. We show that most eigenvalues of the perturbed Toeplitz matrix are at a

    更新日期:2020-09-10
  • Semi-classical analysis of piecewise quasi-polynomial functions and applications to geometric quantization
    Indag. Math. (IF 0.882) Pub Date : 2020-09-06
    Yiannis Loizides; Paul-Emile Paradan; Michele Vergne

    Motivated by applications to multiplicity formulas in index theory, we study a family of distributions Θ(m;k) associated to a piecewise quasi-polynomial function m. The family is indexed by an integer k∈Z>0, and admits an asymptotic expansion as k→∞, which generalizes the expansion obtained in the Euler-Maclaurin formula. When m is the multiplicity function arising from the quantization of a symplectic

    更新日期:2020-09-07
  • Semi-classical mass asymptotics on stationary spacetimes
    Indag. Math. (IF 0.882) Pub Date : 2020-09-06
    Alexander Strohmaier; Steve Zelditch

    We study the spectrum of a timelike Killing vector field Z acting as a differential operator on the solution space Hm:={u∣(□g+m2)u=0} of the Klein-Gordon equation on a globally hyperbolic stationary spacetime (M,g) with compact Cauchy hypersurface Σ. We endow Hm with a natural inner product, so that DZ=1i∇Z is a self-adjoint operator on Hm with discrete spectrum {λj(m)}. In earlier work, we proved

    更新日期:2020-09-07
  • Springer’s work on unipotent classes and Weyl group representations
    Indag. Math. (IF 0.882) Pub Date : 2020-09-03
    G. Lusztig

    We discuss some of the contributions of T.A. Springer (1926–2011) to the theory of algebraic groups, with emphasis on his work on unipotent classes and representations of Weyl groups.

    更新日期:2020-09-03
  • Lines on cubic surfaces, Witt invariants and Stiefel–Whitney classes
    Indag. Math. (IF 0.882) Pub Date : 2020-09-01
    Eva Bayer-Fluckiger; Jean-Pierre Serre

    The aim of this note is to give a formula expressing the trace form associated with the 27 lines of a cubic surface.

    更新日期:2020-09-01
  • Euler-like vector fields, normal forms, and isotropic embeddings
    Indag. Math. (IF 0.882) Pub Date : 2020-09-01
    Eckhard Meinrenken

    As shown in Arnold et al. (1976), germs of tubular neighborhood embeddings for submanifolds N⊆M are in one-one correspondence with germs of Euler-like vector fields near N. In many contexts, this reduces the proof of ‘normal forms results’ for geometric structures to the construction of an Euler-like vector field compatible with the given structure. We illustrate this principle in a variety of examples

    更新日期:2020-09-01
  • Similarity of quadratic and symmetric bilinear forms in characteristic 2
    Indag. Math. (IF 0.882) Pub Date : 2020-08-28
    Detlev W. Hoffmann

    We say that a field extension L∕F has the descent property for isometry (resp. similarity) of quadratic or symmetric bilinear forms if any two forms defined over F that become isometric (resp. similar) over L are already isometric (resp. similar) over F. The famous Artin-Springer theorem states that anisotropic quadratic or symmetric bilinear forms over a field stay anisotropic over an odd degree field

    更新日期:2020-08-28
  • Differentiable spaces that are subcartesian
    Indag. Math. (IF 0.882) Pub Date : 2020-08-15
    Richard Cushman; Jędrzej Śniatycki

    We show that the differential structure of the orbit space of a proper action of a Lie group on an a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian

    更新日期:2020-08-15
  • Non-linear Morse–Bott functions on quaternionic Stiefel manifolds
    Indag. Math. (IF 0.882) Pub Date : 2020-08-14
    Enrique Macías-Virgós; María José Pereira-Sáez; Daniel Tanré

    In the Stiefel manifold Xn,k, we replace Frankel linear height function by a quadratic one. We prove this is still a Morse-Bott function, whose structure of critical levels presents a dichotomy according to the sign of n−2k. The critical submanifolds are no longer Grassmannians but total spaces of fibrations of basis a product of two Grassmannians. We explicitly integrate the gradient flow.

    更新日期:2020-08-14
  • Simplicial cochain algebras for diffeological spaces
    Indag. Math. (IF 0.882) Pub Date : 2020-08-14
    Katsuhiko Kuribayashi

    The original de Rham cohomology due to Souriau and the singular cohomology in diffeology are not isomorphic to each other in general. This manuscript introduces a singular de Rham complex endowed with an integration map into the singular cochain complex which gives the de Rham theorem for every diffeological space. It is also proved that a morphism called the factor map from the original de Rham complex

    更新日期:2020-08-14
  • On factorization of p-adic meromorphic functions
    Indag. Math. (IF 0.882) Pub Date : 2020-08-03
    B. Saoudi; A. Boutabaa; T. Zerzaihi

    In this paper, we study primeness and pseudo primeness of p-adic meromorphic functions. We also consider left (resp. right ) primeness of these functions. We give, in particular, sufficient conditions for a meromorphic function to satisfy such properties. Finally, we consider the problem of permutability of entire functions. We generalize some results in the complex case. However, our method, based

    更新日期:2020-08-03
  • Geometric characterization of preduals of injective Banach lattices
    Indag. Math. (IF 0.882) Pub Date : 2020-07-13
    A.G. Kusraev, S.S. Kutatelatze

    The paper deals with the study of Banach spaces whose duals are injective Banach lattices. Davies in 1967 proved that an ordered Banach space is an L1-predual space if and only if it is a simplex space. In 2007 Duan and Lin proved that a real Banach space is an L1-predual space if and only if its every four-point subset is centerable. We prove the counterparts of these remarkable results for injectives

    更新日期:2020-07-13
  • Continued fraction expansions of the generating functions of Bernoulli and related numbers
    Indag. Math. (IF 0.882) Pub Date : 2020-06-29
    Takao Komatsu

    We give continued fraction expansions of the generating functions of Bernoulli numbers, Cauchy numbers, Euler numbers, harmonic numbers, and their generalized or related numbers. In particular, we focus on explicit forms of the convergents of these continued fraction expansions. Linear fractional transformations of such continued fractions are also discussed. We show more continued fraction expansions

    更新日期:2020-06-29
  • The saddle-point method for general partition functions
    Indag. Math. (IF 0.882) Pub Date : 2020-06-27
    Gregory Debruyne, Gérald Tenenbaum

    We apply the saddle-point method to derive asymptotic estimates or asymptotic series for the number of partitions of a natural integer into parts chosen from a subset of the positive integers whose associated Dirichlet series satisfies certain analytic properties. This enables grouping in a single statement many cases studied in the literature, as well as a number of new ones.

    更新日期:2020-06-27
  • Degeneracy results for fully nonlinear integral operators
    Indag. Math. (IF 0.882) Pub Date : 2020-06-26
    Martin Väth

    It is shown that integral operators of the fully nonlinear type K(x)(t)=∫Ωk(t,s,x(t),x(s))ds exhibit similar degeneracy phenomena in a large class of spaces as superposition operators F(x)(t)=f(t,x(t)). In particular, K is Fréchet differentiable in Lp only if it is affine with respect to the “x(t)” argument. Similar degeneracy results hold if K satisfies a local Lipschitz or compactness condition.

    更新日期:2020-06-26
  • Optimal error estimate of the finite element approximation of second order semilinear non-autonomous parabolic PDEs
    Indag. Math. (IF 0.882) Pub Date : 2020-06-24
    Antoine Tambue, Jean Daniel Mukam

    In this work, numerical approximation of the second order non-autonomous semilinear parabolic partial differential equations (PDEs) is investigated using the classical finite element method. To the best of our knowledge, only the linear case is investigated in the literature. Using an approach based on evolution operator depending on two parameters, we obtain the error estimate of the semi-discrete

    更新日期:2020-06-24
  • Uniform spectral asymptotics for semiclassical wells on phase space loops
    Indag. Math. (IF 0.882) Pub Date : 2020-06-20
    Alix Deleporte; San Vũ Ngọc

    We consider semiclassical self-adjoint operators whose symbol, defined on a two-dimensional symplectic manifold, reaches a non-degenerate minimum b0 on a closed curve. We derive a classical and quantum normal form which gives uniform eigenvalue asymptotics in a window (−∞,b0+ϵ) for ϵ>0 independent on the semiclassical parameter. These asymptotics are obtained in two complementary settings: either an

    更新日期:2020-06-23
  • A note on the moments of sequences of complex numbers
    Indag. Math. (IF 0.882) Pub Date : 2020-06-16
    Maher Boudabra, Greg Markowsky

    We give a short proof that the limsup of the pth root of the modulus of the pth moment of a sequence of complex numbers is equal to the modulus of the maximum of the sequence. This strengthens known results, and provides an analog to a recent result concerning moments of complex polynomials.

    更新日期:2020-06-16
  • Spaces of measurable functions on the Levi-Civita field
    Indag. Math. (IF 0.882) Pub Date : 2020-06-16
    Emanuele Bottazzi

    We introduce the ℒp spaces of measurable functions whose pth power is summable with respect to the uniform measure over the Levi-Civita field. These spaces are the counterparts of the real Lp spaces based upon the Lebesgue measure. Nevertheless, they lack some properties of the Lp spaces: for instance, the ℒp spaces are not sequentially complete with respect to the p-norm. This motivates the study

    更新日期:2020-06-16
  • The 1:2:4 resonance in a particle chain
    Indag. Math. (IF 0.882) Pub Date : 2020-06-09
    Heinz Hanßmann; Reza Mazrooei-Sebdani; Ferdinand Verhulst

    We consider four masses in a circular configuration with nearest-neighbour interaction, generalizing the spatially periodic Fermi–Pasta–Ulam-chain where all masses are equal. We identify the mass ratios that produce the 1:2:4 resonance — the normal form in general is non-integrable already at cubic order. Taking two of the four masses equal allows to retain a discrete symmetry of the fully symmetric

    更新日期:2020-06-09
  • Hardy type inequalities and parametric Lamb equation
    Indag. Math. (IF 0.882) Pub Date : 2020-06-09
    Makarov R.V., Nasibullin R.G.

    This paper is devoted to Hardy type inequalities with remainders for compactly supported smooth functions on open sets in the Euclidean space. We establish new inequalities with weight functions depending on the distance function to the boundary of the domain. One-dimensional L1 and Lp inequalities and their multidimensional analogues are proved. We consider spatial inequalities in open convex domains

    更新日期:2020-06-09
  • On the Riesz dual of L1(μ)
    Indag. Math. (IF 0.882) Pub Date : 2020-06-08
    A. van Rooij

    In this article, (X,A,μ) is a measure apace. A classical result establishes a Riesz isomorphism between L1(μ)∼ and L∞(μ) in case the measure μ is σ-finite. In general, there still is a natural Riesz homomorphism Φ:L∞(μ)→L1(μ)∼, but it may not be injective or surjective. We prove that always the range of Φ is an order dense Riesz subspace of L1(μ)∼. If μ is semi-finite, then L1(μ)∼ is a Dedekind completion

    更新日期:2020-06-08
  • Realizations of holomorphic and slice hyperholomorphic functions: The Krein space case
    Indag. Math. (IF 0.882) Pub Date : 2020-06-01
    Daniel Alpay, Fabrizio Colombo, Irene Sabadini

    In this paper we treat realization results for operator-valued functions which are analytic in the complex sense or slice hyperholomorphic over the quaternions. In the complex setting, we prove a realization theorem for an operator-valued function analytic in a neighborhood of the origin with a coisometric state space operator thus generalizing an analogous result in the unitary case. A main difference

    更新日期:2020-06-01
  • Inverse spectral results for non-abelian group actions
    Indag. Math. (IF 0.882) 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 0.882) 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 (2020, Proposition

    更新日期:2020-05-22
  • Diameter two properties and the Radon–Nikodým property in Orlicz spaces
    Indag. Math. (IF 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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 0.882) 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
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