泛函分析
Let $(X,d)$ be a uniformly locally finite metric space, and $T$ an operator in the uniform Roe algebra $C_u^*(X)$ (or uniform quasi-local algebra $C_{ql}^*(X)$). In this paper, we introduce the concept of limit operators of $T$ on galaxies…
We introduce a topometric version of Lipschitz-free spaces and study its universal property. Another aim of this paper is to investigate actions of topological groups $G$ on Lipschitz-free spaces $\mathcal{F}(M)$, induced by isometric…
We introduce the generalized notion of semicontinuity of a function defined on a topological space and derive the useful classification of the so-called Lipschitz derivatives of functions defined on a metric space. Secondly, we investigate…
In this paper, for $0<\alpha<1$, $p>0$ and positive semidefinite matrices $A,B\ge0$, we consider the quasi-extension $\mathcal{A}_{\alpha,p}(A,B):=((1-\alpha)A^p+\alpha B^p)^{1/p}$ of the $\alpha$-weighted arithmetic matrix mean, and the…
The question of whether the group $\mathbb{Q}_p \rtimes \mathbb{Q}_p^*$ is Hermitian has been stated as an open question in multiple sources in the literature, even as recently as a paper by R. Palma published in 2015. In this note we…
We analyze the embedding properties between Besov spaces, defined on the total space $\mathbb R^n$ and on bounded domains. We give a complete classification on whether or not these embedding maps satisfy certain weak compactness…
We provide an alternative approach to Krasnosel'skii-Precup fixed point theorem for operator systems based on the Leray-Schauder fixed point index in cones. Our focus is on the case of operators whose components are entirely of compressive…
Basis of a Banach space with respect to a filter F on N (F-basis for short) is a generalization of basis, where the ordinary convergence of series is substituted by convergence of partial sums with respect to the filter F. We study the…
For $1\le p<\infty$, let $F^p_\varphi$ be the Fock spaces on ${\mathbb C}^n$ with the weight function $\varphi$ that \(\varphi \in {\mathcal{C}}^{2}\left( {\mathbb{C}}^{n}\right)\) is real-valued and satisfies $ m{\omega }_{0} \leq…
In this study we consider the approximation numbers of differences of composition operators acting on the Hardy-Hilbert space H 2 (D). We obtain both upper and lower bounds for these approximation numbers and by applying these general…
It is known that, if $\Omega$ $\subset$ C is a convex set containing the numerical range of an operator A, then $\Omega$ is a C $\Omega$ -spectral set for A with C $\Omega$ $\le$ 1+ $\sqrt$ 2. We improve this estimate in unbounded cases.
We introduce fractional integrals on the $n$-dimensional spherical cap, study their boundednes in weighted $L^p$ spaces and obtain explicit inversion formulas. The results are applied to the inversion problem for Riesz potentials on a…
In this short note, we study the impact of data augmentation on the smoothness of principal components of high-dimensional datasets. Using tools from quantum harmonic analysis, we show that eigenfunctions of operators corresponding to…
In this paper we characterize $m$-isometric and quasi-$m$-isometric weighted composition operators on the Hilbert space $L^2(\mu)$. Also, we find that normal-$m$-isometry and normal quasi-$m$-isometry weighted composition operators have…
The closed unit bidisc $\overline{\mathbb{D}}^2$ is known to be a spectral set for any pair $(T_1,T_2)$ of commuting contractions. When each $T_i$ is pure and has finite defect, the pair admits a much smaller spectral set: the closure of a…
We establish left and right canonical factorizations of Hilbert-space operator-valued functions G(z) that are analytic on neighborhoods of the complex unit circle and the origin 0, and that have the form G(z)=I+F(z) with F(z) taking…
On the one hand, the framework of mixed norm spaces has potential applications in different areas of mathematics. On the other hand, neural network (NN) operators are well established as approximators, attracting significant attention in…
We investigate operators between spaces of holomorphic functions in several complex variables. Let $G_1, G_2 \subset \mathbb{C}^n$ be cylindrical domains. We construct a canonical map from the space of bounded linear operators…
We investigate multipliers on the space of holomorphic functions $H(\Omega)$, where $\Omega \subset \mathbb{C}^n$ is an open set. For Runge domains, we characterize these multipliers as convolutions with analytic functionals. Additionally,…
Inspired by the work of Bemrose et al. \cite{Be16}, we delve into the study of weaving frames in Krein spaces. This paper presents a comprehensive exploration of various properties and characterizations of Krein space weaving frames. In…