泛函分析

The superposition operators have been widely studied in nonlinear analysis, which are essential for the well-posedness theory of nonlinear equations. In this paper, we investigate the boundedness estimates of superposition operators with…

In the paper, we revisit several approaches to the concept of uniform completion $X^{\mathrm{ru}}$ of a vector lattice $X$. We show that many of these approaches yield the same result. In particular, if $X$ is a sublattice of a uniformly…

We analyze the joint numerical range $W$ of three hermitian matrices of order four. In the generic case, this three-dimensional convex set has a smooth boundary. We analyze non-generic structures. Fifteen possible classes regarding the…

We extend the duality principle for the $\Gamma$-convergence of convex lower semicontinuous functions, which was previously established only in separable reflexive Banach spaces, to the broader class of weakly compactly generated (WCG)…

Let $(X, d, \mu)$ be a space of homogeneous type and $\Omega$ an open subset of $X$. Given a bounded operator $T: L^p(\Omega) \to L^q(\Omega)$ for some $1 \le p \le q < \infty$, we give a criterion for $T$ to be of weak type $(p_0, a)$ for…

A concept of finite-dimensional dynamical system representation is introduced. Since the solution trajectory of partial differential equations are usually represented within infinite-dimensional dynamical systems, the proposed…

We study norm attainment for multilinear operators and homogeneous polynomials between Banach spaces, as well as for positive multilinear operators between Banach lattices. We establish multilinear and polynomial versions of [23, Theorem B]…

We study the weakest convergence-type conditions for fixed point results for Banach and Kannan mappings. Building on Suzuki's weakest condition for Banach mappings and our previous result for Kannan mappings, we compare convergence…

We study the boundedness of averaging projections associated with symmetric Schauder bases in quasi-Banach spaces. Although this property is standard in the Banach setting, it is far from clear in the absence of local convexity and, indeed,…

We obtain a functional model for an arbitrary Abelian locally von Neumann algebra acting on a representing locally Hilbert space under the assumption that the index directed set is countable, in terms of locally essentially bounded…

Littlewood--Paley theory is a fundamental tool for frequency localization, square-function control, and multiplier analysis, yet a systematic counterpart in the fractional Fourier transform (FrFT) setting has remained incomplete. We develop…

We study the existence of positive eigenpairs for a class of Caputo fractional autonomous evolution equations with nonlocal initial condition within the framework of Banach lattices. The autonomous linear operator generates a compact…

This paper aims to study the boundedness and compactness of composition operators from model spaces to the Hardy Hilbert spaces in the upper half-plane. Consequently, we investigate the boundedness and compactness of composition operators…

In this paper, we study perturbation of Hilbert-Schmidt frames under structured modifications, where the perturbation takes the form of replacing finitely or infinitely many frame elements. We establish explicit criteria under which the…

We establish fractional Leibniz rules for the Dunkl Laplacian $\Delta_k$ of the form $$\|(-\Delta_k)^s(fg)\|_{L^p(d\mu_k)} \lesssim \|(-\Delta_k)^s f\|_{L^{p_1}(d\mu_k)} \|g\|_{L^{p_2}(d\mu_k)} + \|f\|_{L^{p_1}(d\mu_k)} \|(-\Delta_k)^s…

For every idempotent $Q$ on a Hilbert space $H$, the matched projection $m(Q)$ is a well-established concept. This paper explores several applications of the matched projections. The first application addresses the distances from…

In our paper we extend some results of the theory of Fourier quasicrystals on the real line to a horizontal strip of finite width. For measures in a strip we use a natural generalization of the usual Fourier transform for measures on the…

We address a number of problems concerning the (im)possibility of either extending locally trivial subbundles of possibly singular Banach/$C^*$ bundles globally, embedding subhomogeneous bundles into homogeneous ones, or recovering locally…

A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in $L^2(\mathbb R)$ was considered by Gabardo and Nashed (J Funct. Anal. 158:209-241, 1998). In this setting, the associated…

The asymptotic properties of negative order pseudo-differential operators have been an important part of the spectral theory since H.Weyl's classical results. In this paper, we derive a spectral asymptotic formula for the negative…