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  • The Plancherel formula for countable groups
    Indag. Math. (IF 0.882) Pub Date : 2021-01-13
    Bachir Bekka

    We discuss a Plancherel formula for countable groups, which provides a canonical decomposition of the regular representation of such a group Γ into a direct integral of factor representations. Our main result gives a precise description of this decomposition in terms of the Plancherel formula of the FC-center Γfc of Γ (that is, the normal sugbroup of Γ consisting of elements with a finite conjugacy

    更新日期:2021-01-13
  • Stinespring’s theorem for unbounded operator valued local completely positive maps and its applications
    Indag. Math. (IF 0.882) Pub Date : 2021-01-12
    B.V. Rajarama Bhat; Anindya Ghatak; P. Santhosh Kumar

    Dosiev (2008) obtained a Stinespring’s theorem for local completely positive maps (in short: local CP-maps) on locally C∗-algebras. In this article a suitable notion of minimality for this construction has been identified so as to ensure uniqueness up to unitary equivalence for the associated representation. Using this a Radon–Nikodym type theorem for local completely positive maps has been proved

    更新日期:2021-01-12
  • Pointwise lineability in sequence spaces
    Indag. Math. (IF 0.882) Pub Date : 2021-01-02
    Daniel Pellegrino; Anselmo Raposo

    We continue the research on lineability/spaceability properties in sequence spaces. Our main results show that several theorems in this framework are valid in a stricter sense. To do this job we introduce the notion of pointwise lineability which seems to be of independent interest for further investigations in other environments.

    更新日期:2021-01-02
  • Diego’s Theorem for nuclear implicative semilattices
    Indag. Math. (IF 0.882) Pub Date : 2020-12-24
    G. Bezhanishvili; N. Bezhanishvili; L. Carai; D. Gabelaia; S. Ghilardi; M. Jibladze

    We prove that the variety of nuclear implicative semilattices is locally finite, thus generalizing Diego’s Theorem. The key ingredients of our proof include the coloring technique and construction of universal models from modal logic. For this we develop duality theory for finite nuclear implicative semilattices, generalizing Köhler duality. We prove that our main result remains true for bounded nuclear

    更新日期:2020-12-25
  • Spherical functions for Gelfand pairs of complex reflection groups
    Indag. Math. (IF 0.882) Pub Date : 2020-12-24
    Robin van Haastrecht

    In this article the zonal spherical functions of the Gelfand pair (G(r,d,n),Sn) of complex reflection groups will be calculated. After this, a product formula for these spherical functions and a discrete analogue of the Laplace operator which has the spherical functions as eigenfunctions will be given.

    更新日期:2020-12-25
  • The irreducibility of some Wronskian Hermite polynomials
    Indag. Math. (IF 0.882) Pub Date : 2020-12-17
    Codruţ Grosu; Corina Grosu

    We study the irreducibility in Z[x] of Wronskian Hermite polynomials labelled by partitions. It is known that these polynomials factor as a power of x times a remainder polynomial. We show that the remainder polynomial is irreducible for the partitions (n,m) with m≤2, and (n,n) when n+1 is a square. Our main tools are two theorems that we prove for all partitions. The first result gives a sharp upper

    更新日期:2020-12-17
  • Self-adjointness of perturbed bi-Laplacians on infinite graphs
    Indag. Math. (IF 0.882) Pub Date : 2020-12-17
    Ognjen Milatovic

    We give a sufficient condition for the essential self-adjointness of a perturbation of the square of the magnetic Laplacian on an infinite weighted graph. The main result is applicable to graphs whose degree function is not necessarily bounded. The result allows perturbations that are not necessarily bounded from below by a constant.

    更新日期:2020-12-17
  • Hamiltonian and reversible systems with smooth families of invariant tori
    Indag. Math. (IF 0.882) Pub Date : 2020-12-13
    Mikhail B. Sevryuk

    For various values of n, d, and the phase space dimension, we construct simple examples of Hamiltonian and reversible systems possessing smooth d-parameter families of invariant n-tori carrying conditionally periodic motions. In the Hamiltonian case, these tori can be isotropic, coisotropic, or atropic (neither isotropic nor coisotropic). The cases of non-compact and compact phase spaces are considered

    更新日期:2020-12-14
  • Remarks on results by Müger and Tuset on the moments of polynomials
    Indag. Math. (IF 0.882) Pub Date : 2020-12-05
    Greg Markowsky; Dylan Phung

    Let f(x) be a non-zero polynomial with complex coefficients, and Mp=∫01f(x)pdx for p a positive integer. In a recent paper, Müger and Tuset showed that lim supp→∞|Mp|1∕p>0, and conjectured that this limit is equal to the maximum amongst the critical values of f together with the values |f(0)| and |f(1)|. We give an example that shows that this conjecture is false. It also may be natural to guess that

    更新日期:2020-12-07
  • Remark on norm compactness in Lp(μ,X)
    Indag. Math. (IF 0.882) Pub Date : 2020-12-05
    Youcef Askoura

    We prove a compactness criterion in Lp(μ,X): a subset of Lp(μ,X) is relatively norm compact iff the set of integrals of its functions over any measurable set is relatively norm compact, it satisfies the Fréchet oscillation restriction condition and it is p-uniformly integrable. The proof is elementary.

    更新日期:2020-12-07
  • Ergodic decomposition
    Indag. Math. (IF 0.882) Pub Date : 2020-11-10
    Sakshi Jain; Shah Faisal

    Ergodic systems, being indecomposable are important part of the study of dynamical systems but if a system is not ergodic, it is natural to ask the following question: Is it possible to split it into ergodic systems in such a way that the study of the former reduces to the study of latter ones? Also, it will be interesting to see if the latter ones inherit some properties of the former one. This document

    更新日期:2020-11-12
  • Minuscule embeddings
    Indag. Math. (IF 0.882) Pub Date : 2020-11-07
    Benedict H. Gross; Skip Garibaldi

    We study embeddings J→G of simple linear algebraic groups with the following property: the simple components of the J module Lie(G)∕Lie(J) are all minuscule representations of J. One family of examples occurs when the group G has roots of two different lengths and J is the subgroup generated by the long roots. We classify all such embeddings when J=SL2 and J=SL3, show how each embedding implies the

    更新日期:2020-11-09
  • On additive and multiplicative decompositions of sets of integers with restricted prime factors, I. (Smooth numbers)
    Indag. Math. (IF 0.882) Pub Date : 2020-11-06
    K. Győry; L. Hajdu; A. Sárközy

    In Sárközy (2001) the third author of this paper presented two conjectures on the additive decomposability of the sequence of ”smooth” (or ”friable”) numbers. Elsholtz and Harper (2015) proved (by using sieve methods) the second (less demanding) conjecture. The goal of this paper is to extend and sharpen their result in three directions by using a different approach (based on the theory of S-unit equations)

    更新日期:2020-11-06
  • 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:2020-11-03
  • 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:2020-11-03
  • 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:2020-11-03
  • 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:2020-11-03
  • 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:2020-11-03
  • 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:2020-11-03
  • 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:2020-11-03
  • 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 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:2020-11-03
  • A Thom isomorphism in foliated de Rham theory
    Indag. Math. (IF 0.882) Pub Date : 2020-11-02
    Yi Lin; Reyer Sjamaar

    We prove a Thom isomorphism theorem for differential forms in the setting of transverse Lie algebra actions on foliated manifolds and foliated vector bundles.

    更新日期:2020-11-02
  • Generating subgroups of the circle using a generalized class of density functions
    Indag. Math. (IF 0.882) Pub Date : 2020-10-31
    Pratulananda Das; Ayan Ghosh

    In this article, we consider the generalized version dgf of the natural density function introduced in Bose et al. (2018) where g:N→[0,∞) satisfies g(n)→∞ and ng(n)↛0 whereas f is an unbounded modulus function and generate versions of characterized subgroups of the circle group T using these density functions. We show that these subgroups have the same feature as the s-characterized subgroups (Dikranjan

    更新日期:2020-11-02
  • 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
  • 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
  • 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
  • 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
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