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Reciprocals of Weighted Composition Operators in $$L^2$$ -Spaces Results Math. (IF 2.2) Pub Date : 2024-03-16 Piotr Budzyński
Various formulas for reciprocals of densely defined weighted composition operators in \(L^2\)-spaces as well as for their adjoints are provided. The relation between the reciprocal of a weighted composition operator and the product of the reciprocals of the associated multiplication operator and composition operator is studied.
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A Generalized Von Neumann’s Theorem for Linear Relations in Hilbert Spaces Results Math. (IF 2.2) Pub Date : 2024-03-16
Abstract Assume that \({\mathfrak {X}}\) is a real or complex Hilbert space, T a linear relation in \({\mathfrak {X}}\) and B a bounded linear operator in \({\mathfrak {X}}\) , whose adjoints are denoted by \(T^{*}\) and \(B^{*}\) , respectively. It is shown in this note that if the following four linear relations \(TBB^{*}T^{*}\) , \(B^{*}T^{*}TB\) , \(BTT^{*}B^{*}\) and \(T^{*}B^{*}BT\) are selfadjoint
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Paired Kernels and Their Applications Results Math. (IF 2.2) Pub Date : 2024-03-16 M. Cristina Câmara, Jonathan R. Partington
This paper considers paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space \(H^2\). The kernels of such operators, together with their analytic projections, which are generalizations of Toeplitz kernels, are studied. Results on near-invariance properties, representations, and inclusion relations for these kernels are obtained. The existence
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On the Multiplicity of Solutions of a Discrete Robin Problem with Variable Exponents Results Math. (IF 2.2) Pub Date : 2024-03-09
Abstract In this paper, we prove the existence and multiplicity of solutions of a discrete Robin problem with variable exponents in a T-dimensional Banach space. The proofs of our main results are based on variational methods.
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Preservation of Order and Orthogonality on Preduals of Jordan Algebras Results Math. (IF 2.2) Pub Date : 2024-03-09 E. Chetcuti, J. Hamhalter
We study linear maps between preduals of JBW-algebras that preserve orthogonal decompositions of functionals. We generalize and strengthen results of Bunce and Wright (Pac J Math 158(2):265–272, 1993) obtained for von Neumann algebras by characterizing continuous orthogonally decomposable linear maps between preduals of JBW-algebras. In particular, we show that Banach space adjoint of such morphism
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Uniformity and Loewner Condtions of Metric Spaces Results Math. (IF 2.2) Pub Date : 2024-03-09 Xiantao Wang, Zhiqiang Yang
In this paper, we establish four equivalent conditions in the metric space setting. These conditions concern the (inner) uniformity of metric spaces, and (locally) Loewner conditions, weak slice conditions and k-cap conditions of metric measure spaces. This investigation completes the related study started by Bonk, Heinonen, and Koskela in 2001. Also, two examples are constructed to demonstrate that
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Mutual-Visibility Sets in Cartesian Products of Paths and Cycles Results Math. (IF 2.2) Pub Date : 2024-03-09
Abstract For a given graph G, the mutual-visibility problem asks for the largest set of vertices \(M \subseteq V(G)\) with the property that for any pair of vertices \(u,v \in M\) there exists a shortest u, v-path of G that does not pass through any other vertex in M. The mutual-visibility problem for Cartesian products of a cycle and a path, as well as for Cartesian products of two cycles, is considered
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Global Multiplicity of Positive Solutions for Nonlinear Robin Problems with an Indefinite Potential Term Results Math. (IF 2.2) Pub Date : 2024-03-02 Eylem Öztürk, Nikolaos S. Papageorgiou
We consider a Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction is parametric and exhibits the competing effects of a concave (sublinear) and of a convex (superlinear) terms (“concave-convex” problem). The parameter multiplies the convex term. We prove an existence and multiplicity theorem which is global in parameter.
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The e-Property of Asymptotically Stable Markov Semigroups Results Math. (IF 2.2) Pub Date : 2024-03-02 Ryszard Kukulski, Hanna Wojewódka-Ścia̧żko
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Interpolator Symmetries and New Kalton-Peck Spaces Results Math. (IF 2.2) Pub Date : 2024-02-28 Jesús M. F. Castillo, Willian H. G. Corrêa, Valentin Ferenczi, Manuel González
We study the six diagrams generated by the first three Schechter interpolators \(\Delta _2(f)= f''(1/2)/2!, \Delta _1(f)= f'(1/2), \Delta _0(f)=f(1/2)\) acting on the Calderón space associated to the pair \((\ell _\infty , \ell _1)\). We will study the remarkable and somehow unexpected properties of all the spaces appearing in those diagrams: two new spaces (and their duals), two Orlicz spaces (and
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On the Second Pinching Theorem for Willmore Hypersurfaces in a Sphere Results Math. (IF 2.2) Pub Date : 2024-02-28 Haizhong Li, Meng Zhang
In this paper, we consider n-dimensional compact Willmore hypersurface in a unit sphere. We prove a pinching theorem of \(\rho ^2\), which is defined as \(\rho ^2=S-nH^2\), for n-dimensional compact Willmore hypersurface with constant mean curvature and constant scalar curvature, where H denotes the mean curvature and S the squared norm of the second fundamental form of this hypersurface.
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General Position Polynomials Results Math. (IF 2.2) Pub Date : 2024-02-28 Vesna Iršič, Sandi Klavžar, Gregor Rus, James Tuite
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Width of Convex Bodies in Hyperbolic Space Results Math. (IF 2.2) Pub Date : 2024-02-28 Marek Lassak
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Semi-classical Orthogonal Polynomials Associated with a Modified Gaussian Weight Results Math. (IF 2.2) Pub Date : 2024-02-24 Yadan Ding, Chao Min
We are concerned with the monic orthogonal polynomials with respect to the modified Gaussian weight $$\begin{aligned} w(x)=w(x;s):=\textrm{e}^{-N[x^2+s(x^6-x^2)]},\qquad x\in \mathbb {R} \end{aligned}$$ with parameters \(N> 0\) and \(s\in [0,1]\). Using the ladder operator approach and associated compatibility conditions, we show that the recurrence coefficient \(\beta _n(s)\) satisfies a nonlinear
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Fourier Transform Decay of Distributions in Hardy–Morrey Spaces Results Math. (IF 2.2) Pub Date : 2024-02-24 Marcelo F. de Almeida, Tiago Picon
We establish decay estimates for Fourier transform on Hardy–Morrey spaces and its localizable version. Our work includes some aspects to these spaces linked up with pointwise Fourier estimates, in particular a natural approach on cancellation moment conditions. As application, we discuss the optimality for continuity of Fourier multipliers and pseudodifferential operators in Hardy–Morrey spaces.
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Lebedev–Skalskaya Transform Related Continuous Wavelet Transform Results Math. (IF 2.2) Pub Date : 2024-02-24 Ajay K. Gupt, U. K. Mandal, Akhilesh Prasad
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Connection Between Weighted Tail, Orlicz, Grand Lorentz And Grand Lebesgue Norms Results Math. (IF 2.2) Pub Date : 2024-02-24 Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
We prove that the norm of functions in a suitable Grand Lorentz space built on a measure space, equipped with sigma finite diffuse measure, coincides with the norm in a suitable exponential Grand Lebesgue Space space as well as coincides with the so-called exponential tail norm, which may be quite described as norm in a suitable Banach rearrangement invariant space. We also exhibit comparisons with
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The Minimal Function of a BV Function Results Math. (IF 2.2) Pub Date : 2024-02-24
Abstract In this paper we introduce a class of one dimensional non-centered minimal operator \({\widetilde{m}}_\Phi \) associated to a function \(\Phi \) , which covers the usual minimal operator. We establish the boundedness of \({\widetilde{m}}_\Phi :\textrm{BV}(\mathbb {R})\rightarrow \textrm{BV}(\mathbb {R})\) under a more restrictive condition on \(\Phi \) . Here \(\textrm{BV}(\mathbb {R})\) is
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Derivation of Specific Solutions and Asymptotic Analysis for the Cylindrical Dirichlet Problem Results Math. (IF 2.2) Pub Date : 2024-02-24
Abstract In this paper, we deduce a new formula that explicitly expresses the cylindrical Poisson kernel of any degree and order using cylindrical Poisson polynomials. We then demonstrate how this formula can be applied to solve the Dirichlet boundary value problems for cylindrical Laplace equations. Furthermore, we examine and discuss the behaviors of this solution approach at infinity.
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The Anti-symmetric Solution of the Matrix Equation $$AXA^\top =B$$ on a Null Subspace Results Math. (IF 2.2) Pub Date : 2024-02-24 Shanshan Hu, Yongxin Yuan
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Plane Polynomials and Hamiltonian Vector Fields Determined by Their Singular Points Results Math. (IF 2.2) Pub Date : 2024-02-24 John A. Arredondo, Jesús Muciño-Raymundo
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On Distribution of Rice–Middleton Model Results Math. (IF 2.2) Pub Date : 2024-02-24
Abstract The probability density function in Rice–Middleton model, which describes the behavior of the single sinusoidal random signal combined with Gaussian noise is expressed in three mutually independent ways: firstly, with the aid of an integral representation of the modified Bessel function of the first kind of integer order; secondly, by a hyperbolic cosine differential operator and thirdly,
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Compactness Criteria for Stieltjes Function Spaces and Applications Results Math. (IF 2.2) Pub Date : 2024-02-22 Francisco J. Fernández, F. Adrián F. Tojo, Carlos Villanueva
In this work we study some topological aspects of function spaces arising in Stieltjes differential calculus. Chief among them are compactness results related to the Ascoli–Arzelà and Kolmogorov–Riesz theorems, as well as their applications to Stieltjes-Sobolev spaces and decomposable functions.
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A New Extension of Van Hamme’s (E.2) Supercongruence Results Math. (IF 2.2) Pub Date : 2024-02-22 Chenying Wang
By means of the creative microscoping method introduced by Guo and Zudilin, we establish some q-supercongruences. As conclusions, we obtain new one-parameter generalizations of Van Hamme’s (E.2) supercongruence and a similar result due to Swisher.
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Characterizations of Composition Operators on Bloch and Hardy Type Spaces Results Math. (IF 2.2) Pub Date : 2024-02-14 Shaolin Chen, Hidetaka Hamada
The main purpose of this paper is to investigate characterizations of composition operators on Bloch and Hardy type spaces. Initially, we use general doubling weights to study the composition operators from harmonic Bloch type spaces on the unit disc \({\mathbb {D}}\) to pluriharmonic Hardy spaces on the Euclidean unit ball \({\mathbb {B}}^n\). Furthermore, we develop some new methods to study the
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Isoparametric Hypersurfaces of Riemannian Manifolds as Initial Data for the Mean Curvature Flow Results Math. (IF 2.2) Pub Date : 2024-02-14 Felippe Guimarães, João Batista Marques dos Santos, João Paulo dos Santos
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Counterintuitive Patterns on Angles and Distances Between Lattice Points in High Dimensional Hypercubes Results Math. (IF 2.2) Pub Date : 2024-02-10
Abstract Let \({\mathcal {S}}\) be a finite set of integer points in \({\mathbb {R}}^d\) , which we assume has many symmetries, and let \(P\in {\mathbb {R}}^d\) be a fixed point. We calculate the distances from P to the points in \({\mathcal {S}}\) and compare the results. In some of the most common cases, we find that they lead to unexpected conclusions if the dimension is sufficiently large. For
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Transposed Poisson Structures Results Math. (IF 2.2) Pub Date : 2024-02-10 Patrícia Damas Beites, Bruno Leonardo Macedo Ferreira, Ivan Kaygorodov
To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is given.
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Sums of Squares on Hypersurfaces Results Math. (IF 2.2) Pub Date : 2024-02-05
Abstract We show that the Pythagoras number of rings of type \({\mathbb {R}}[x,y, \sqrt{f(x,y)}]\) is infinite, provided that the polynomial f(x, y) satisfies some mild conditions.
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A New Look at Old Theorems of Fejér and Hardy Results Math. (IF 2.2) Pub Date : 2024-02-05 Vladimir Mikhailets, Aleksandr Murach, Oksana Tsyhanok
The article studies the convergence of trigonometric Fourier series via a new Tauberian theorem for Cesàro summable series in abstract normed spaces. This theorem generalizes some known results of Hardy and Littlewood for number series. We find sufficient conditions for the convergence of trigonometric Fourier series in homogeneous Banach spaces over the circle. These conditions are expressed in terms
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A New q-Variation of the (C.2) Supercongruence of Van Hamme Results Math. (IF 2.2) Pub Date : 2024-02-05 Victor J. W. Guo
Long proved that Van Hamme’s (C.2) supercongruence is also true modulo \(p^4\) for any prime \(p>3\). By making use of the q-WZ method, the author and Wang gave a q-analogue of Long’s supercongruence. In this paper, employing the method of ‘creative microscoping’, introduced by the author and Zudilin in 2019, we obtain a generalization of this q-supercongruence. A limiting case of our result implies
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Coneability of Anti-Fubini Functions and Other Lineability Properties Results Math. (IF 2.2) Pub Date : 2024-02-05 L. Bernal-González, M. C. Calderón-Moreno, G. A. Muñoz-Fernández, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepúlveda
It is proved that the family of measurable real functions on the product measure space satisfying (or not) the conclusion of Fubini’s Theorem (along with a number of related families) is algebraically large, in the sense that it contains large convex cones or even large vector subspaces (except for zero) under rather general assumptions. Several earlier related results are improved, mainly regarding
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Well-Posedness in Gevrey Function Space for the 3D Axially Symmetric MHD Boundary Layer Equations Without Structural Assumption Results Math. (IF 2.2) Pub Date : 2024-02-05 Xueyun Lin, Lin Zou
In this paper, we establish the well-posedness theory for the three-dimensional axially symmetric magnetohydrodynamic (MHD) boundary layer system in Gevrey function space without any structural assumption. By using a refined cancellation mechanism to overcome the loss of tangential derivatives in the system and constructing a refined energy functional involves in a polynomial weight on the tangential
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Normal Critical Surfaces in $${\mathbb {C}}P^{2}$$ Results Math. (IF 2.2) Pub Date : 2024-02-05
Abstract Let \(F: M\rightarrow {\mathbb {C}}P^{2}\) be an isometric immersion of a closed surface in the complex projective plane \({\mathbb {C}}P^{2}\) . In this paper, we consider the functional \(W_{N}(F)=\int _{M}({\overline{K}}^{\perp }-K^{\perp })\textrm{d}M\) , which is a global conformal invariant. The critical surfaces of \(W_{N}(F)\) are called normal critical surfaces. We compute the first
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Lower Characteristic, Weakly Quasi-compact and Application Results Math. (IF 2.2) Pub Date : 2024-01-31 Sami Baraket, Aref Jeribi
In this paper, we present some results concerning the weakly quasi-compact and lower characteristic operators. An application to Markov chains, is given.
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A Pre-adjoint Approach on Weighted Composition Operators Between Spaces of Lipschitz Functions Results Math. (IF 2.2) Pub Date : 2024-01-28 Arafat Abbar, Clément Coine, Colin Petitjean
We consider weighted composition operators, that is operators of the type \(g \mapsto w \cdot g \circ f\), acting on spaces of Lipschitz functions. Bounded weighted composition operators, as well as some compact weighted composition operators, have been characterized quite recently. In this paper, we provide a different approach involving their pre-adjoint operators, namely the weighted Lipschitz operators
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On the Equivalence in ZF+BPI of the Hahn–Banach Theorem and Three Classical Theorems Results Math. (IF 2.2) Pub Date : 2024-01-25
Abstract The presented paper is a compendium or a kind of précis of relationships between the four classical theorems of mathematical analysis. More precisely, the first aim of this paper is to present the equivalence of the four classical theorems: the Hahn–Banach theorem, the Mazur–Orlicz theorem, the Markov–Kakutani fixed-point theorem and the von Neumann theorem on amenability of Abelian groups
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p-Kirchhoff Modified Schrödinger Equation with Critical Nonlinearity in $$\mathbb {R}^{N}$$ Results Math. (IF 2.2) Pub Date : 2024-01-25 Sihua Liang, Han Liu, Deli Zhang
This article study the following on p-Kirchhoff modified Schrödinger equation with critical nonlinearity in \(\mathbb {R}^{N}\): $$\begin{aligned} {\mathcal {K}}(u)+V(x)|u{{|}^{p-2}}u= & {} \lambda \left( \int _{{{\mathbb {R}}^{N}}}{\frac{|u(y){{|}^{2p_{\mu }^{*}}}}{|y-x{{|}^{\mu }}}dy} \right) |u(x){{|}^{2p_{\mu }^{*}-2}}u(x)\\{} & {} +f(x,u) \text{ in }\ \mathbb {R}^{N}, \end{aligned}$$ where \({\mathcal
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Generalized Dual Hilbert–Schmidt Frames and Their Topological Properties Results Math. (IF 2.2) Pub Date : 2024-01-23 Rui-Qi Dong, Yun-Zhang Li
This paper addresses the Hilbert–Schmidt frame (HS-frame) theory. We introduce the concept of generalized dual HS-frame (g-dual HS-frame) which generalizes that of g-dual frame. We prove that two equivalent HS-frames form a g-dual HS-frame pair, characterize operators on \(\ell ^2\) that transform a pair of HS-Riesz bases into a g-dual HS-frame pair, and present a parametric expression of all g-dual
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On Unigraphic Polyhedra with One Vertex of Degree $${p-2}$$ Results Math. (IF 2.2) Pub Date : 2024-01-23
Abstract A sequence \(\sigma \) of p non-negative integers is unigraphic if it is the degree sequence of exactly one graph, up to isomorphism. A polyhedral graph is a 3-connected, planar graph. We investigate which sequences are unigraphic with respect to the class of polyhedral graphs, meaning that they admit exactly one realisation as a polyhedron. We focus on the case of sequences with largest entry
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Generalized Chain Rules and Applications to Stieltjes Differential and Integral Equations Results Math. (IF 2.2) Pub Date : 2024-01-23 Ignacio Márquez Albés, Antonín Slavík
We present new generalizations of the chain rule, which involve Stieltjes derivatives and integrals. The results are subsequently used to obtain the power rules for two generalizations of the exponential function, and to investigate Bernoulli-type equations with Stieltjes derivatives and integrals.
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Norm Attaining Elements of the Ball Algebra $$H^\infty (B_N)$$ Results Math. (IF 2.2) Pub Date : 2024-01-23 Richard M. Aron, José Bonet, Manuel Maestre
Let \(B_N\) be the Euclidean ball of \({\mathbb {C}}^N\). The space \(H^\infty (B_N)\) of bounded holomorphic functions on \(B_N\) is known to have a predual, denoted by \(G^\infty (B_N)\). We study the functions in \(H^\infty (B_N)\) that attain their norm as elements of the dual of \(G^\infty (B_N)\). We also examine similar questions for the polydisc algebra \(H^\infty ({\mathbb {D}}^N)\) and for
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Isometric Models of the Funk Disc and the Busemann Function Results Math. (IF 2.2) Pub Date : 2024-01-23
Abstract In this article, we find three isometric models of the Funk disc: Finsler upper half of the hyperboloid of two sheets model, the Finsler band model and the Finsler upper hemi sphere model; and we also find two new models of the Finsler–Poincaré disc. We explicitly describe the geodesics in each model. Moreover, we compute the Busemann function and consequently describe the horocycles in the
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The Minimal Spectral Radius with Given Independence Number Results Math. (IF 2.2) Pub Date : 2024-01-23
Abstract In this paper, we determine the graphs which have the minimal spectral radius among all the connected graphs of order n and the independence number \(\lceil \frac{n}{2}\rceil -1.\)
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Inequalities for Convex Functions and Isotonic Sublinear Functionals Results Math. (IF 2.2) Pub Date : 2024-01-20 Zdzisław Otachel
In this paper, versions of the famous Jensen inequality for sublinear isotonic functionals are proved. The obtained results generalize classic Jessen’s and McShane’s inequalities. Applications to generalized means and to Hölder’s and Minkowski’s inequalities are also given.
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Ahlfors–David Regular Sets, Point Spectrum and Dirichlet Spaces Results Math. (IF 2.2) Pub Date : 2024-01-20 O. El-Fallah, Y. Elmadani, I. Labghail
Let E be a closed subset of the unit circle \(\mathbb {T}\), and let \(\alpha \in (0,1)\). Nikolski’s result states that if the Hausdorff dimension of E is strictly greater than \(\alpha \), then for any operator T on a separable Hilbert space such that the point spectrum \(\sigma _p(T)\) of T contains E, the series \(\sum _{n}n^{\alpha -1}\Vert T^n\Vert ^{-2}\) converges. A partial converse of this
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AMHNMH, AMNM and ADND Pairs Results Math. (IF 2.2) Pub Date : 2024-01-20 Bahman Hayati, Hamid Khodaei
Let A be a Banach algebra, let X and Y be Banach A-modules and take \({\mathfrak {B}}(X, Y)\) as the space of all bounded linear maps from X into Y. The pair \((X, Y)_A\) is said to be an AMHNMH if almost module homomorphisms are near module homomorphisms in the norm topology on \({\mathfrak {B}}(X, Y)\). We study AMHNMH pairs and give some examples of them. As a result, we prove that if A is amenable
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On Dimension of Fractal Functions on Product of the Sierpiński Gaskets and Associated Measures Results Math. (IF 2.2) Pub Date : 2024-01-20 Rattan Lal, Bilel Selmi, Saurabh Verma
In this article, our aim is to estimate the fractal dimensions of the graphs of fractal interpolation functions (FIFs) on the product of two Sierpiński gaskets. To achieve this, we employ the Hölder function spaces. We also define a fractal operator on Hölder spaces originated from the FIFs and establish some operator-theoretic properties such as bounded below and invariant subspaces of it. Additionally
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Zak Transform Associated with the Weyl Transform and the System of Twisted Translates on $$\mathbb {R}^{2n}$$ Results Math. (IF 2.2) Pub Date : 2024-01-13 Radha Ramakrishnan, Rabeetha Velsamy
We introduce the Zak transform on \(L^{2}(\mathbb {R}^{2n})\) associated with the Weyl transform. By making use of this transform, we define a bracket map and prove that the system of twisted translates \(\{{T_{(k,l)}^t}{\phi }: k,l\in \mathbb {Z}^{n}\}\) is a frame sequence iff \(0
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New Multivariate and Univariate Aldaz–Kounchev–Render Type Operators Results Math. (IF 2.2) Pub Date : 2024-01-13 Dumitru Popa
We introduce and study new multivariate and univariate Aldaz–Kounchev–Render type operators including their convergence and the asymptotic expansions. We solve also in the positive a conjecture from the very recent paper of Acu A. M., De Marchi S., Rasa I. (Result Math 78(1):21, 2023).
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Approximation Theorems for Complex $$\alpha $$ -Bernstein–Kantorovich Operators Results Math. (IF 2.2) Pub Date : 2024-01-13 M. Kara, N. I. Mahmudov
In this paper, we introduce the complex form of \(\alpha \)-Bernstein–Kantorovich operators. Respectively, upper quantitative estimates for the complex \(\alpha \)-Bernstein–Kantorovich operator and its derivatives, Voronovskaya type result and the exact order of approximation of these operators are studied.
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Hypersurfaces of the Space form for Which the Covariant Derivative of Their Ricci Tensors has Vanishing Minimal Norm Tensor Results Math. (IF 2.2) Pub Date : 2024-01-13 Zhen Guo, Hong Li
In this paper, we first calculate for a Riemannian manifold the minimal norm tensor of the covariant derivative of the Ricci curvature. Then we show that, for an n-dimensional (\(n\geqslant 4\)) umbilic-free hypersurface of the space form, if the covariant derivative of the Ricci curvature has vanishing minimal norm tensor, it has parallel Ricci curvature or it is a special rotational hypersurface
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Approximation by Multivariate Max-Product Kantorovich Exponential Sampling Operators Results Math. (IF 2.2) Pub Date : 2024-01-13 Sathish Kumar Angamuthu
Abstract The approximation behavior of multivariate max-product Kantorovich exponential sampling operators has been analyzed. The point-wise and uniform approximation theorem for these sampling series \(I^{\chi ,(M)}_{\textbf{w},j}\) is proved. The degree of approximation in-terms of logarithmic modulus of smoothness is studied. For the class of log-Hölderian functions, the order of uniform norm convergence
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Hyers–Ulam Stability for a Type of Discrete Hill Equation Results Math. (IF 2.2) Pub Date : 2024-01-13 Douglas R. Anderson, Masakazu Onitsuka
We establish the Hyers–Ulam stability of a second-order linear Hill-type h-difference equation with a periodic coefficient. Using results from first-order h-difference equations with periodic coefficient of arbitrary order, both homogeneous and non-homogeneous, we also establish a Hyers–Ulam stability constant. Several interesting examples are provided. As a powerful application, we use the main result
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Parabolicity on Graphs Results Math. (IF 2.2) Pub Date : 2024-01-13 Álvaro Martínez-Pérez, José M. Rodríguez
Large scale properties of Riemannian manifolds, in particular, those properties preserved by quasi-isometries, can be studied using discrete structures which approximate the manifolds. In a sequence of papers, M. Kanai proved that, under mild conditions, many properties are preserved by a certain (quasi-isometric) graph approximation of a manifold. One of these properties is p-parabolicity. A manifold
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Convergence in Law of Iterates of Weakly Contractive in Mean Random-Valued Functions Results Math. (IF 2.2) Pub Date : 2024-01-13 Karol Baron, Rafał Kapica, Janusz Morawiec
We investigate the asymptotic behaviour of the sequence of forward type iterations of a given random-valued vector function on the state space being a separable and complete metric space. Assuming non-linear contraction in mean we prove that the considered sequence converges weakly to a random variable with a finite first moment and independent of the initial state. Moreover, we show that the speed
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Stability of Wave Equation with Variable Coefficients by Boundary Fractional Dissipation Law Results Math. (IF 2.2) Pub Date : 2024-01-13 Hui Ge, Zhifei Zhang
In this paper, we consider the boundary stability of the wave equation with variable coefficients and fractional damping acting on part of the boundary. The acceleration terms on the boundary are involved as well. It has been known that the presence of such dynamic structures on the boundary may change drastically the stability property of the underlying system. We obtain the polynomial decay for the
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Polynomial Equations for Additive Functions I: The Inner Parameter Case Results Math. (IF 2.2) Pub Date : 2024-01-12 Eszter Gselmann, Gergely Kiss
The aim of this sequence of work is to investigate polynomial equations satisfied by additive functions. As a result of this, new characterization theorems for homomorphisms and derivations can be given. More exactly, in this paper the following type of equation is considered $$\begin{aligned} \sum _{i=1}^{n}f_{i}(x^{p_{i}})g_{i}(x^{q_{i}})= 0 \qquad \left( x\in \mathbb {F}\right) , \end{aligned}$$
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Packing a Tetrahedron by Similar Tetrahedra Results Math. (IF 2.2) Pub Date : 2024-01-12 Janusz Januszewski, Łukasz Zielonka
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Pointwise Gradient Estimates and Sobolev Boundedness for Commutators of Fractional New Maximal Operators Results Math. (IF 2.2) Pub Date : 2024-01-12 Rui Li, Shuangping Tao
In this article, we consider the Sobolev boundedness for the commutators of fractional new maximal operators both in the global and local settings. More precisely, in the global case, we prove that \(M_{b,\varphi ,\beta }\) and \([b,{M}_{\varphi ,\beta }]\) are bounded on Sobolev space \(W^{1,q}(\mathbb {R}^{n})\); in the local case, the boundedness for \(M_{b,\varphi ,\beta ,\Omega }\) and \([b,{M}_{\varphi