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  • Generalized Balian–Low Theorem Associated with the Linear Canonical Transform
    Results Math. (IF 1.162) Pub Date : 2020-07-24
    Zhichao Zhang

    Linear canonical transform (LCT), which is of importance in solving differential equations and analyzing optical systems, extends the conventional Fourier transform to the time-frequency domain characterized by a parameter matrix \(\mathbf{A }=(a,b;c,d)\). The main objective of this paper is to study the Balian–Low theorem in the LCT domain. We first state a Balian–Low theorem associated with the LCT

    更新日期:2020-07-24
  • Szász–Mirakjan–Kantorovich Operators Reproducing Affine Functions
    Results Math. (IF 1.162) Pub Date : 2020-07-24
    Jorge Bustamante

    We present a new Kantorovich modification of Szász–Mirakjan operators which reproduce affine functions. We present an upper estimate for the rate of convergence of the new operators in polynomial weighted spaces and characterized all functions for which there is convergence.

    更新日期:2020-07-24
  • Co-Isometric Weighted Composition Operators on Hilbert Spaces of Analytic Functions
    Results Math. (IF 1.162) Pub Date : 2020-07-18
    María J. Martín, Alejandro Mas, Dragan Vukotić

    We obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric on a general weighted Hardy space of analytic functions in the unit disk whose reproducing kernel has the usual natural form. This turns out to be equivalent to the property of being unitary. The result reveals a dichotomy identifying a specific family of weighted Hardy spaces as the only ones that

    更新日期:2020-07-18
  • Almost Geodesics and Special Affine Connection
    Results Math. (IF 1.162) Pub Date : 2020-07-17
    Olga Belova, Josef Mikeš

    In the present paper we continue to study almost geodesic curves and determine in \({\mathbb {R}}^n\) the form of curves \({\mathcal {C}}\) for which every image under an \((n-1)\)-dimensional algebraic torus is also an almost geodesic with respect to an affine connection \(\nabla \) with constant coefficients. We also calculate explicitly the components of \(\nabla \). For the explicit calculation

    更新日期:2020-07-17
  • Gauss–Bonnet Theorems in the BCV Spaces and the Twisted Heisenberg Group
    Results Math. (IF 1.162) Pub Date : 2020-07-17
    Yong Wang, Sining Wei

    In this paper, we compute sub-Riemannian limits of Gaussian curvature for a Euclidean \(C^2\)-smooth surface in the BCV spaces and the twisted Heisenberg group away from characteristic points and signed geodesic curvature for Euclidean \(C^2\)-smooth curves on surfaces. We get Gauss–Bonnet theorems in the BCV spaces and the twisted Heisenberg group.

    更新日期:2020-07-17
  • Characterizations of Gelfand Rings Specially Clean Rings and their Dual Rings
    Results Math. (IF 1.162) Pub Date : 2020-07-16
    Mohsen Aghajani, Abolfazl Tarizadeh

    In this paper, new criteria for zero dimensional rings, Gelfand rings, clean rings and mp-rings are given. A new class of rings is introduced and studied, we call them purified rings. Specially, reduced purified rings are characterized. New characterizations for pure ideals of reduced Gelfand rings and mp-rings are provided. It is also proved that if the topology of a scheme is Hausdorff, then the

    更新日期:2020-07-16
  • D -homothetically Deformed K -contact Ricci Almost Solitons
    Results Math. (IF 1.162) Pub Date : 2020-07-15
    Nagaraja H. Gangadharappa, Ramesh Sharma

    If a K-contact manifold (M, g) and a D-homothetically deformed K-contact manifold \((M,{\bar{g}})\) are both Ricci almost solitons with the same associated vector field V, then we show (i) that (M, g) and (\(M, {\bar{g}}\)) are both D-homothetically fixed \(\eta \)-Einstein Ricci solitons, and (ii) V preserves \(\phi \). We also show that, if the associated vector field V of a complete K-contact Ricci

    更新日期:2020-07-15
  • Variations on a Theme of Glauberman
    Results Math. (IF 1.162) Pub Date : 2020-07-13
    Tim Penttila, Alessandro Siciliano

    A new and elementary proof of the Artin–Zorn theorem that finite alternative division rings are fields is given. The characterisation of finite fields of Glauberman and Heimbeck is also extended to a broader class of fields, the two subjects being connected via geometry.

    更新日期:2020-07-13
  • Harmonic Spaces and Density Functions
    Results Math. (IF 1.162) Pub Date : 2020-07-11
    P. B. Gilkey, J. H. Park

    We use the density function of a harmonic space to obtain estimates for the eigenvalues of the Jacobi operator; when these estimates are sharp, then the harmonic space is a symmetric Osserman space.

    更新日期:2020-07-13
  • The Poincare Lemma, Antiexact Forms, and Fermionic Quantum Harmonic Oscillator
    Results Math. (IF 1.162) Pub Date : 2020-07-11
    Radosław Antoni Kycia

    The paper focuses on various properties and applications of the homotopy operator, which occurs in the Poincaré lemma. In the first part, an abstract operator calculus is constructed, where the exterior derivative is an abstract derivative and the homotopy operator plays the role of an abstract integral. This operator calculus can be used to formulate abstract differential equations. An example of

    更新日期:2020-07-13
  • Approximation by Complex Perturbed Bernstein-Type Operators
    Results Math. (IF 1.162) Pub Date : 2020-07-10
    Ana-Maria Acu, Gülen Başcanbaz-Tunca

    In this paper we consider complex form of a modified (perturbed) Bernstein operators attached to an analytic function in a disk of radius \(R>1\) centered at the origin. We obtain quantitative estimates of the convergence in compact disks and exact degree of simultaneous approximation with the help of upper estimates in quantitative form, and of lower estimates obtained from a qualitative Voronovskaja

    更新日期:2020-07-10
  • Harmonic SU (3)- and $$G_2$$ G 2 -Structures via Spinors
    Results Math. (IF 1.162) Pub Date : 2020-07-09
    Kamil Niedziałomski

    In this note, using the spinorial description of SU(3) and \(G_2\)-structures obtained recently by other authors, we give necessary and sufficient conditions for harmonicity of the above mentioned structures. We describe the results on appropriate homogeneous spaces. Here, harmonicity means harmonicity of a certain unique section induced by the G-structure in consideration.

    更新日期:2020-07-09
  • Direct and Inverse Results for Kantorovich Type Exponential Sampling Series
    Results Math. (IF 1.162) Pub Date : 2020-07-09
    Sathish Kumar Angamuthu, Shivam Bajpeyi

    In this article, we analyse the behaviour of the new family of Kantorovich type exponential sampling series. We derive the point-wise approximation theorem and Voronovskaya type theorem for the series \((I_{w}^{\chi })_{w>0}.\) Further, we establish a representation formula and an inverse result of approximation for these operators. Finally, we give some examples of kernel functions to which the theory

    更新日期:2020-07-09
  • Superlinear Perturbations of the Eigenvalue Problem for the Robin Laplacian Plus an Indefinite and Unbounded Potential
    Results Math. (IF 1.162) Pub Date : 2020-07-09
    Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš

    We consider a superlinear perturbation of the eigenvalue problem for the Robin Laplacian plus an indefinite and unbounded potential. Using variational tools and critical groups, we show that when \(\lambda \) is close to a nonprincipal eigenvalue, then the problem has seven nontrivial solutions. We provide sign information for six of them.

    更新日期:2020-07-09
  • On Double- k -Systems of Spheres
    Results Math. (IF 1.162) Pub Date : 2020-07-09
    Hiroshi Maehara, Horst Martini

    An oriented sphere in \({\mathbb {R}}^n\) is a sphere for which one side (inside or outside) is distinguished as its positive side. Two oriented spheres are said to be properly tangent if they are tangent and the positive side of one sphere is contained in the positive side of the other. A set of 2k spheres \(\{\alpha _1,\dots ,\alpha _k,\beta _1,\dots ,\beta _k\}\) in \({\mathbb {R}}^n\) is called

    更新日期:2020-07-09
  • On the Closest to Zero Roots and the Second Quotients of Taylor Coefficients of Entire Functions from the Laguerre–Pólya I Class
    Results Math. (IF 1.162) Pub Date : 2020-07-09
    Thu Hien Nguyen, Anna Vishnyakova

    For an entire function \(f(z) = \sum _{k=0}^\infty a_k z^k, a_k>0\), we show that if f belongs to the Laguerre–Pólya class, and the quotients \(q_k:= \frac{a_{k-1}^2}{a_{k-2}a_k}, k=2, 3, \ldots \) satisfy the condition \(q_2 \le q_3\), then f has at least one zero in the segment \([-\frac{a_1}{a_2},0]\). We also give necessary conditions and sufficient conditions of the existence of such a zero in

    更新日期:2020-07-09
  • Semi-discrete Quantitative Voronovskaya-Type Theorems for Positive Linear Operators
    Results Math. (IF 1.162) Pub Date : 2020-07-09
    Sorin G. Gal

    Because all the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor’s formula which is a very particular case of Lagrange–Hermite interpolation formula, in this paper we obtain semi-discrete quantitative Voronovskaya-type theorems based on various other Lagrange–Hermite interpolation formulas. Applications to Bernstein–Kantorovich and

    更新日期:2020-07-09
  • On Magnetic Curves in Almost Cosymplectic Sol Space
    Results Math. (IF 1.162) Pub Date : 2020-07-05
    Zlatko Erjavec, Jun-ichi Inoguchi

    Magnetic curves with respect to the almost cosymplectic structure of the \(\mathrm {Sol}_3\) space are determined and curvature properties of these curves are investigated.

    更新日期:2020-07-05
  • The m -Hessian Operator on Some Weighted Energy Classes of Delta m -Subharmonic Functions
    Results Math. (IF 1.162) Pub Date : 2020-07-05
    V. V. Hung, H. N. Quy

    In this paper, we construct a topology on the vector space \(\delta \mathcal F_{m,\chi }(\Omega )\). We also prove that with this topology it is quasi-Banach, non-separable and non-reflexive. We also give a characterization for the class \(\mathcal F_{m, \min \{\chi _1, \chi _2\}}(\Omega )\).

    更新日期:2020-07-05
  • On Hyperbolic Affine Generalized Infinite Iterated Function Systems
    Results Math. (IF 1.162) Pub Date : 2020-07-04
    Alexandru Mihail, Silviu-Aurelian Urziceanu

    The aim of this paper is to provide alternative characterizations of hyperbolic affine generalized infinite iterated function systems. More precisely, we prove that, for such a system \({\mathcal {F}}=((X,\left\| .\right\| ),(f_{i})_{i\in I})\), among others, the following statements are equivalent: (a) \({\mathcal {F}}\) is hyperbolic. (b) \( {\mathcal {F}}\) has attractor. (c) \({\mathcal {F}}\)

    更新日期:2020-07-05
  • A Remark on Dilation-and-Modulation Frames for $${L^2({\pmb {\mathbb {R}}_+)}}$$ L 2 ( R + )
    Results Math. (IF 1.162) Pub Date : 2020-07-03
    Jakob Lemvig

    We show that every rationally sampled dilation-and-modulation system is unitarily equivalent to a multi-window Gabor system with special structures. As a consequence, the study of dilation-and-modulation systems in \(L^2({\mathbb {R}}_+)\) reduces to that of multi-window Gabor systems in \(L^2({\mathbb {R}})\) with special structures.

    更新日期:2020-07-03
  • On Sharpness of Error Bounds for Univariate Approximation by Single Hidden Layer Feedforward Neural Networks
    Results Math. (IF 1.162) Pub Date : 2020-07-01
    Steffen Goebbels

    A new non-linear variant of a quantitative extension of the uniform boundedness principle is used to show sharpness of error bounds for univariate approximation by sums of sigmoid and ReLU functions. Single hidden layer feedforward neural networks with one input node perform such operations. Errors of best approximation can be expressed using moduli of smoothness of the function to be approximated

    更新日期:2020-07-01
  • New Inequalities for the Coefficients of Unimodular Bounded Functions
    Results Math. (IF 1.162) Pub Date : 2020-07-01
    Saminathan Ponnusamy, Ramakrishnan Vijayakumar, Karl-Joachim Wirths

    The classical inequality of Bohr asserts that if a power series converges in the unit disk and its sum has modulus less than or equal to 1, then the sum of absolute values of its terms is less than or equal to 1 for the subdisk \(|z|<1/3\) and 1/3 is the best possible constant. Recently, there has been a number of investigations on this topic. In this article, we present related inequalities using

    更新日期:2020-07-01
  • On a $$\rho $$ ρ -Orthogonally Additive Mappings
    Results Math. (IF 1.162) Pub Date : 2020-07-01
    Jacek Chmieliński, Justyna Sikorska, Paweł Wójcik

    We show that a real normed linear space endowed with the \(\rho \)-orthogonality relation, in general need not be an orthogonality space in the sense of Rätz. However, we prove that \(\rho \)-orthogonally additive mappings defined on some classical Banach spaces have to be additive. Moreover, additivity (and approximate additivity) under the condition of an approximate orthogonality is considered.

    更新日期:2020-07-01
  • On Complete Conformally Flat Submanifolds with Nullity in Euclidean Space
    Results Math. (IF 1.162) Pub Date : 2020-06-27
    Christos-Raent Onti

    In this note, we investigate conformally flat submanifolds of Euclidean space with positive index of relative nullity. Let \(M^n\) be a complete conformally flat manifold and let \(f:M^n\rightarrow \mathord {\mathbb {R}}^m\) be an isometric immersion. We prove the following results: (1) If the index of relative nullity is at least two, then \(M^n\) is flat and f is a cylinder over a flat submanifold

    更新日期:2020-06-27
  • A Note on Integrability of the Norm of a Perturbed Semigroup
    Results Math. (IF 1.162) Pub Date : 2020-06-17
    Adam Bobrowski

    Recently, Michael Gil’ has provided a condition for integrability of norms of semigroups generated by operators of the form \(A+B\) where B is bounded, in terms of the norm of the commutator of A and B. We show that his argument, when slightly refined, leads to a bit more general result than the one presented in his paper. We also argue, by examining an example, that the size of the commutator may

    更新日期:2020-06-17
  • Products of Volterra Type Operators and Composition Operators Between Fock Spaces
    Results Math. (IF 1.162) Pub Date : 2020-06-16
    Pham Trong Tien

    We show that entire functions \(\varphi \), which induce bounded products of Volterra integral operators \(V_g\) (Volterra companion operators \(J_g\)) and composition operators \(C_{\varphi }\) acting between different Fock spaces, must be affine functions, i.e. \(\varphi (z) = az + b\). Then, using this special form of \(\varphi \), we characterize boundedness and compactness of these products in

    更新日期:2020-06-16
  • Surjectivity, Closed Range, and Fredholmness of the Composition and Multiplication Operators Between Possibly Distinct Orlicz Spaces
    Results Math. (IF 1.162) Pub Date : 2020-06-16
    Tadeusz Chawziuk, Yousef Estaremi, Henryk Hudzik

    We give criteria for the closely related concepts of surjectivity, closed range, and Fredholmness of the composition and multiplication operators between possibly different Orlicz spaces over non-atomic measure spaces.

    更新日期:2020-06-16
  • Generating a Probability Measure from a Fractal Structure
    Results Math. (IF 1.162) Pub Date : 2020-06-15
    J. F. Gálvez-Rodríguez, M. A. Sánchez-Granero

    Fractal structures were introduced to characterize non-archimedean quasi-metrization, and there is a strong relationship between these two concepts. In this paper we show how to define a probability measure with the help of a fractal structure, by taking advantage of its recursive nature. One of the keys of this approach is the use of the completion of the fractal structure. Since we want to define

    更新日期:2020-06-15
  • An Application of Medial Limits to Iterative Functional Equations
    Results Math. (IF 1.162) Pub Date : 2020-06-15
    Janusz Morawiec

    Assume that \((\Omega ,{\mathcal {A}},P)\) is a probability space, \(f:[0,1]\times \Omega \rightarrow [0,1]\) is a function such that \(f(0,\omega )=0\), \(f(1,\omega )=1\) for every \(\omega \in \Omega \), \(g:[0,1]\rightarrow \mathbb R\) is a bounded function such that \(g(0)=g(1)=0\), and \(a,b\in \mathbb R\). Applying medial limits we describe bounded solutions \(\varphi :[0,1]\rightarrow \mathbb

    更新日期:2020-06-15
  • Dynamical Systems of the p -Adic (2, 2)-Rational Functions with Two Fixed Points
    Results Math. (IF 1.162) Pub Date : 2020-06-13
    U. A. Rozikov, I. A. Sattarov

    We consider a family of (2, 2)-rational functions given on the set of complex p-adic field \(\mathbb C_p\). Each such function f has two distinct fixed points \(x_1=x_1(f)\), \(x_2=x_2(f)\). We study p-adic dynamical systems generated by the (2, 2)-rational functions. We prove that \(x_1\) is always an indifferent fixed point for f, i.e., \(x_1\) is a center of some Siegel disk \(SI(x_1)\). Depending

    更新日期:2020-06-13
  • A Geometrical Characterization of Proportionally Modular Affine Semigroups
    Results Math. (IF 1.162) Pub Date : 2020-06-13
    J. D. Díaz-Ramírez, J. I. García-García, A. Sánchez-R.-Navarro, A. Vigneron-Tenorio

    A proportionally modular affine semigroup is the set of nonnegative integer solutions of a modular Diophantine inequality \(f_1x_1+\cdots +f_nx_n \bmod b \le g_1x_1+\cdots +g_nx_n\), where \(g_1,\dots ,g_n\), \(f_1,\ldots ,f_n\in \mathbb {Z}\), and \(b\in \mathbb {N}\). In this work, a geometrical characterization of these semigroups is given. On the basis of this geometrical approach, some algorithms

    更新日期:2020-06-13
  • Alienation and the Stability Problem
    Results Math. (IF 1.162) Pub Date : 2020-06-08
    Justyna Sikorska

    Starting from the inequality $$\begin{aligned} |f(x+y)-f(x)-f(y)+g(x+y)-g(x)g(y)|\leqslant \varepsilon , \quad x,y\in S, \end{aligned}$$ where f is a complex valued function defined on a monoid S, we deal with two problems: the stability problem and the problem of alienation of the approximate additivity condition from the condition of approximate exponentiality.

    更新日期:2020-06-08
  • On $$\widetilde{J}$$J~ -tangent Affine Hyperspheres
    Results Math. (IF 1.162) Pub Date : 2020-06-04
    Zuzanna Szancer

    In this paper we study \(\widetilde{J}\)-tangent affine hyperspheres, where \(\widetilde{J}\) is the canonical para-complex structure on \(\mathbb {R}^{2n+2}\). The main purpose of this paper is to give a classification of \(\widetilde{J}\)-tangent affine hyperspheres of an arbitrary dimension with an involutive distribution \(\mathcal {D}\). In particular, we classify all such hyperspheres in the

    更新日期:2020-06-04
  • Urysohn Type Schurer Operators
    Results Math. (IF 1.162) Pub Date : 2020-06-04
    Murat Bodur, Harun Karsli, Fatma Taşdelen

    This paper deals with the Urysohn type integral form of the Schurer operators which is a significant special class of operators that act on some function spaces. Firstly, we construct the Urysohn type Schurer operators and after that we obtain some convergence results for the aforementioned operators. Ultimately, we deal with some of their shape-preserving properties.

    更新日期:2020-06-04
  • Second Homotopy Group and Invariant Geometry of Flag Manifolds
    Results Math. (IF 1.162) Pub Date : 2020-06-03
    Lino Grama, Lucas Seco

    We use the Hopf fibration to explicitly compute generators of the second homotopy group of the flag manifolds of a compact Lie group. We show that these 2-spheres have nice geometrical properties such as being totally geodesic surfaces with respect to any invariant metric on the flag manifold, generalizing a result in Burstall and Rawnsley (Springer Lect. Notes Math. 2(84):1424, 1990). This illustrates

    更新日期:2020-06-03
  • A Note on Doubly Commuting Tuples of Hyponormal Operators on Hilbert Spaces
    Results Math. (IF 1.162) Pub Date : 2020-06-03
    Kais Feki

    Our aim in this paper is to prove the equality between two kinds of joint operator norms in the case of doubly commuting tuples of hyponormal operators on Hilbert spaces. Moreover, a sharp bound for the distance between two doubly commuting tuples of hyponormal operators in terms of the distance between their Harte spectra is proved.

    更新日期:2020-06-03
  • One-Sided Hyperbolicity via Evolution Maps
    Results Math. (IF 1.162) Pub Date : 2020-06-03
    Luis Barreira, Claudia Valls

    We give characterizations of the hyperbolicity of a nonautonomous one-sided dynamics defined by a sequence of linear operators, in terms of the hyperbolicity of an associated evolution map defined on a Banach space of sequences. We consider a large family of spaces of sequences besides \(L^p\) spaces. Moreover, we discuss the general cases when the dynamics may be invertible only along the unstable

    更新日期:2020-06-03
  • Bounds of Non-real Eigenvalues for Indefinite p -Laplacian Problems
    Results Math. (IF 1.162) Pub Date : 2020-06-02
    Fu Sun

    The present paper deals with the non-real eigenvalues of one dimensional p-Laplacian problem with an indefinite weight. The upper bounds on the imaginary parts and the absolute values of non-real eigenvalues for this indefinite p-Laplacian problem with Dirichlet boundary conditions are obtained through a new method, partly inspired by the estimates obtained in Kikonko and Mingarelli (J Differ Equ 261:6221–6232

    更新日期:2020-06-02
  • New Trace Formulae for Sturm–Liouville Operators on the Lasso-Graph
    Results Math. (IF 1.162) Pub Date : 2020-06-02
    Sheng-Yu Guan, Chuan-Fu Yang

    The Sturm–Liouville operators on the lasso graph are considered. We obtain new regularized trace formulae for this class of differential operators, which are very useful to further study the inverse spectral problems of this kind of operators.

    更新日期:2020-06-02
  • Regularity Properties of Bilinear Maximal Function and Its Fractional Variant
    Results Math. (IF 1.162) Pub Date : 2020-06-02
    Feng Liu, Suying Liu, Xiao Zhang

    We introduce and study the bilinear fractional maximal operator $$\begin{aligned} {\mathfrak {M}}_\alpha (f,g)(x)=\sup \limits _{r>0}\frac{1}{|B(O,r)|^{1-\frac{\alpha }{n}}}\int _{B(O,r)}|f(x+y)g(x-y)|dy,\ \ \ \ \ x\in {\mathbb {R}}^n, \end{aligned}$$ where \(O=(0,0,\ldots ,0)\in {\mathbb {R}}^n\) and \(0\le \alpha

    更新日期:2020-06-02
  • On Set-Valued Solutions of a Generalized Bi-quadratic Functional Equation
    Results Math. (IF 1.162) Pub Date : 2020-06-02
    Iz-iddine EL-Fassi, El-Sayed El-Hady, Kazimierz Nikodem

    In this article, we obtain a characterizations and representations of set-valued solutions defined on an Abelian group G with values in a Hausdorff topological vector space of the following generalized bi-quadratic functional equation: $$\begin{aligned}&F(x+y,z+w)+F(x+y,z-w)+F(x-y,z+w)+F(x-y,z-w) \\&\quad =aF(x,z)+bF(x,w)+cF(y,z)+dF(y,w), \end{aligned}$$ for some nonnegative real numbers a, b, c, and

    更新日期:2020-06-02
  • Blow-up and Lifespan of Solutions for a Nonlinear Viscoelastic Kirchhoff Equation
    Results Math. (IF 1.162) Pub Date : 2020-06-02
    Zhifeng Yang

    The blow-up of solutions of a class of nonlinear viscoelastic Kirchhoff equation with suitable initial data and Dirichlet boundary conditions is discussed. By constructing a suitable auxiliary function to overcome the difficulty of gradient estimation and making use of differential inequality technique, we establish a finite time blow-up result when the initial data is at arbitrary energy level. Moreover

    更新日期:2020-06-02
  • Envelope of Intermediate Lines of a Plane Curve
    Results Math. (IF 1.162) Pub Date : 2020-06-02
    Ady Cambraia, Mostafa Salarinoghabi, Diego Trindade

    For a pair of points in a smooth closed convex planar curve \(\gamma \), its mid-line is the line containing its mid-point and the intersection point of the corresponding pair of tangent lines. It is well known that the envelope of the mid-lines (EML) is formed by the union of three affine invariants sets: Affine envelope symmetry sets; mid-parallel tangent locus and affine evolute of \(\gamma \).

    更新日期:2020-06-02
  • Conjugacy Problem of Strictly Monotone Maps with Only One Jump Discontinuity
    Results Math. (IF 1.162) Pub Date : 2020-06-02
    Jinghua Liu, Yong-Guo Shi

    The conjugacy problem is one of the important questions in iteration theory. As far as we know, for discontinuous strictly monotone maps there is no complete result. In this paper, we investigate the conjugacy problem of strictly monotone maps with only one jump discontinuity. We give some sufficient and necessary conditions for the conjugacy relationship. And we present some methods to construct all

    更新日期:2020-06-02
  • The Varchenko Determinant for Apartments
    Results Math. (IF 1.162) Pub Date : 2020-06-02
    Hery Randriamaro

    Varchenko introduced a distance function on chambers of hyperplane arrangements that he called quantum bilinear form. That gave rise to a determinant indexed by chambers whose entry in position (C, D) is the distance between C and D: that is the Varchenko determinant. He showed that that determinant has a nice factorization. Later, Aguiar and Mahajan defined a generalization of the quantum bilinear

    更新日期:2020-06-02
  • Invariant Submanifolds of Paracontact Metric $$(\tilde{\kappa }\ne -1, \tilde{\mu })$$(κ~≠-1,μ~) -Manifolds
    Results Math. (IF 1.162) Pub Date : 2020-06-02
    Irem Küpeli Erken

    The principal objective of this paper is to answer positively the open question whether every invariant submanifold of a paracontact metric \(( \tilde{\kappa },\tilde{\mu })\)-manifold is totally geodesic. Main result is that any invariant submanifold of a paracontact metric \((\tilde{\kappa }, \tilde{\mu })\)-manifold,\(\tilde{\kappa }\ne -1\), is always totally geodesic. Additionally, if \(\tilde{\kappa

    更新日期:2020-06-02
  • Disjoint Distributional Chaos in Fréchet Spaces
    Results Math. (IF 1.162) Pub Date : 2020-05-24
    Marko Kostić

    We introduce two different notions of disjoint distributional chaos for sequences of continuous linear operators in Fréchet spaces. We focus special attention to the analysis of some specific classes of linear continuous operators having a certain disjoint distributionally chaotic behaviour, providing also a great number of illustrative examples and applications of our abstract theoretical results

    更新日期:2020-05-24
  • Functions Preserving the Biadditivity
    Results Math. (IF 1.162) Pub Date : 2020-05-23
    Radosław Łukasik, Paweł Wójcik

    In this paper we consider the generalization of the orthogonality equation. Let S be a semigroup, and let H, X be abelian groups. For two given biadditive functions \(A:S^2\rightarrow X\), \(B:H^2\rightarrow X\) and for two unknown mappings \(f,g:S\rightarrow H\) the functional equation $$\begin{aligned} B(f(x),g(y))=A(x,y) \end{aligned}$$ will be solved under quite natural assumptions. This extends

    更新日期:2020-05-23
  • Conjugate Linear Maps from C $$^*$$∗ -Algebras into Their Dual Spaces which are Ternary Derivable at the Unit Element
    Results Math. (IF 1.162) Pub Date : 2020-05-23
    Zakiye Khalili, Mohammad Reza Miri, Mohsen Niazi

    We prove that every continuous conjugate linear mapping from a unital C\(^*\)-algebra A into its dual space, \(A^*\), which is ternary derivable at the unit element of A is a ternary derivation. This is somehow a ternary-counterpart result for (binary) derivations on associative algebras which proves that any linear continuous map from a unital C\(^*\)-algebra A into a Banach A-bimodule which is derivable

    更新日期:2020-05-23
  • Voronovskaja Type Theorems for King Type Operators
    Results Math. (IF 1.162) Pub Date : 2020-05-23
    Dumitru Popa

    We introduce and study the King type operators associated to a couple \( \left( \mathcal {A},\tau \right) \) where \(\mathcal {A}=\left( A_{n}\right) _{n\in \mathbb {N}}\) is a sequence of linear positive operators from \(C\left[ 0,1\right] \) into \(C\left[ 0,1\right] \) and \(\tau :\left[ 0,1\right] \rightarrow \left[ 0,\infty \right) \) a continuous strictly increasing function. Given a sequence

    更新日期:2020-05-23
  • Functions with Ultradifferentiable Powers
    Results Math. (IF 1.162) Pub Date : 2020-05-19
    Vincent Thilliez

    We study the regularity of smooth functions f defined on an open subset of \({\mathbb {R}}^n\) and such that, for certain integers \(p\ge 2\), the powers \(f^p :x\mapsto (f(x))^p\) belong to a Denjoy–Carleman class \({\mathcal {C}}_M\) associated with a suitable weight sequence M. Our main result is a statement analogous to a classic theorem of H. Joris on \({\mathcal {C}}^\infty \) functions: if a

    更新日期:2020-05-19
  • Proof of Some q -Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial
    Results Math. (IF 1.162) Pub Date : 2020-05-15
    Victor J. W. Guo

    We prove some q-supercongruences modulo the fourth power of a cyclotomic polynomial by making use of the Chinese remainder theorem for coprime polynomials, Watson’s \(_8\phi _7\) transformation, and the ‘creative microscoping’ method introduced by the author and Wadim Zudilin. In particular, we confirm Conjecture 1.5 in (Results Math 74:131, 2019).

    更新日期:2020-05-15
  • On the eigenvalues and the torsional rigidities of regular Reuleaux polygons
    Results Math. (IF 1.162) Pub Date : 2020-05-15
    G. A. Philippin

    Let \(\lambda _1({\tilde{R}}_{2n+1})\) be the first Dirichlet eigenvalues of the Laplacian associated to regular Reuleaux polygons \({\tilde{R}}_{2n+1}\) of width \({\tilde{w}}_{2n+1}=1\), \(n=1,2,3,\ldots \)Let \(T({\tilde{R}}_{2n+1})\) be their torsional rigidities. It is established that \(\lambda _1({\tilde{R}}_{2n+1})\) is a decreasing sequence, and \(T({\tilde{R}}_{2n+1})\) an increasing sequence

    更新日期:2020-05-15
  • Spacelike Hypersurfaces Immersed in Weighted Standard Static Spacetimes: Uniqueness, Nonexistence and Stability
    Results Math. (IF 1.162) Pub Date : 2020-04-29
    Eudes L. de Lima, Henrique F. de Lima, André F. A. Ramalho, Marco A. L. Velásquez

    A spacetime endowed with a globally defined timelike Killing vector field admits a certain model of warped product, called the standard static spacetime, and, when the volume element is modified by a factor that depends on a smooth function (which is called density function), we say that this ambient is a weighted standard static spacetime. In such spacetimes, we study some aspects of the geometry

    更新日期:2020-04-29
  • D’Alembert’s Functional Equations on Monoids with an Anti-endomorphism
    Results Math. (IF 1.162) Pub Date : 2020-04-25
    Mohamed Ayoubi, Driss Zeglami

    Let M be a topological monoid. Our main goal is to introduce the functional equation $$\begin{aligned} g(xy)+\mu (y)g(x\psi (y))=2g(x)g(y),\ \ x,y\in M, \end{aligned}$$ where \(\psi :M\rightarrow M\) is a continuous anti-endomorphism that need not be involutive and \(\mu :M\rightarrow \mathbb {C}\) is a continuous multiplicative function such that \(\mu (x\psi (x))=1\) for all \(x\in M\). We exploit

    更新日期:2020-04-25
  • Regularity of the Solution of the Scalar Signorini Problem in Polygonal Domains
    Results Math. (IF 1.162) Pub Date : 2020-04-25
    Thomas Apel, Serge Nicaise

    The Signorini problem for the Laplace operator is considered in a general polygonal domain. It is proved that the coincidence set consists of a finite number of boundary parts plus a finite number of isolated points. The regularity of the solution is described. In particular, we show that the leading singularity is in general \(r_i^{\pi /(2\alpha _i)}\) at transition points of Signorini to Dirichlet

    更新日期:2020-04-25
  • Characterization of Inner Product Spaces by Strongly Schur-Convex Functions
    Results Math. (IF 1.162) Pub Date : 2020-04-24
    Mirosław Adamek

    Involving the notion of strongly Schur-convex functions we give a new characterization of inner product spaces among norm spaces. We also present a representation theorem for functions which generate strongly Schur-convex sums.

    更新日期:2020-04-24
  • Some q -supercongruences from Watson’s $$_8\phi _7$$8ϕ7 Transformation Formula
    Results Math. (IF 1.162) Pub Date : 2020-04-24
    Xiaoxia Wang, Mingbing Yue

    Recently, Jana and Kalita proved the following supercongruences involving rising factorials \((\frac{1}{d})_k^3\): $$\begin{aligned}&\sum _{k=0}^{N} (-1)^k (2dk+1)\frac{(\frac{1}{d})_k^3}{k!^3}\\&\quad \equiv {\left\{ \begin{array}{ll} p^r&{}\pmod {p^{r+2}},\quad \text {if } r \text { is even};\\ (-1)^{\frac{(p-d+1)r}{d}}(d-1)p^r&{}\pmod {p^{r+2}},\quad \text {if } r \text { is odd}; \end{array}\right

    更新日期:2020-04-24
  • Weyl–Schrödinger Representations of Heisenberg Groups in Infinite Dimensions
    Results Math. (IF 1.162) Pub Date : 2020-04-24
    Oleh Lopushansky

    We investigate the group \({\mathcal {H}}_{\mathbb {C}}\) of complexified Heisenberg matrices with entries from an infinite-dimensional complex Hilbert space H. Irreducible representations of the Weyl–Schrödinger type on the space \(L^2_\chi \) of quadratically integrable \({\mathbb {C}}\)-valued functions are described. Integrability is understood with respect to the projective limit \(\chi =\varprojlim

    更新日期:2020-04-24
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