泛函分析

We obtain large sieve type inequalities for the Rayleigh quotient of the restriction of phase space representations of higher rank operators, via an operator analogue of the short-time Fourier transform (STFT). The resulting bounds are…

In the present paper, we study quantum Sobolev spaces whose elements are operators of the Hilbert-Schmidt class. We construct these Sobolev spaces from the Fourier transform for operators. Next, we obtain continuous embedding theorems.…

On a volume doubling metric measure space endowed with a family of $p$-energies such that the Poincar\'e inequality and the cutoff Sobolev inequality with $p$-walk dimension $\beta_p$ hold, for $p$ in an open interval $I\subseteq…

Bessel potential spaces have gained renewed interest due to their robust structural properties and applications in fractional partial differential equations (PDEs). These spaces, derived through complex interpolation between Lebesgue and…

The dynamics of weighted translation operators on Lebesgue spaces, Orlicz spaces, and in general on solid Banach function spaces have been studied in numerous papers. Recently, the dynamics of weighted translations on weighted Orlicz spaces…

We will solve a problem by Aliaga and Perneck\'a about Lipschitz free spaces (denoted by $\mathcal F(M)$): $$\text{Does every Borel measure $\mu$ on a complete metric space $M$ such that $\int d(m,0) d |\mu|(m)< \infty$ induce a weak$^*$…

In this article, we study the similarity of the Polish operator topologies $\texttt{WOT}$, $\texttt{SOT}$, $\texttt{SOT}\mbox{$_{*}$}$ and $\texttt{SOT}\mbox{$^{*}$}$ on the set of the positive contractions on $\ell_p$ with $p > 1$. Using…

In this paper, we first study some elementary properties of a typical positive contraction on $\ell_q$ for the Strong Operator Topology and the Strong* Operator Topology. Using these properties, we prove that a typical positive contraction…

We introduce and study the directional Stockwell transform as a hybrid of the directional short-time Fourier transform and the ridgelet transform. We prove an extended Parseval identity and a reconstruction formula for this transform, as…

We develop a new functional-analytic technique for investigating the degree of noncompactness of an operator defined on a quasinormed space and taking values in a Marcinkiewicz space. The main result is a general principle from which it can…

Let $\mathcal{L}$ be the special Hermite operator on $\mathbb{C}^n$. As a continuation of the recent results in \cite{SG}, we establish new Strichartz estimates for systems of orthonormal functions associated with general flows of the form…

The study presents a vector-valued extension of the classical Mercer theorem within the framework of reproducing kernel Hilbert spaces defined over Kaplansky-Hilbert modules associated with the algebra of essentially bounded measurable…

Let $\Phi$ be an (LB)-space over $\mathbb F=\mathbb R$ or $\mathbb C$, and let $\Phi'$ be the dual space of~$\Phi$. We study the set $\mathbb S(\Phi)$ of Sheffer operators acting in polynomials on $\Phi'$. We prove that $\mathbb S(\Phi)$ is…

We extend the deformation to the normal cone and tangent groupoid constructions from finite-dimensional manifolds to infinite-dimensional Banach and Fredholm manifolds. Next, we generalize the concept of Fredholm filtrations to get a more…

Bounded composition operators in Paley-Wiener spaces have simple forms, and they are just operators composed through affine mappings of the complex plane. The purpose of this article is to explore some notions about bounded operators and…

In connection with the Fuglede conjecture, we study the existence of commuting self-adjoint extensions of the partial differential operators on arbitrary, possibly disconnected domains in $\br^d$, the associated unitary group, the spectral…

Given two variable exponent Muckenhoupt weights $w\in A_{p(\cdot)}$ and $w_1\in A_{p_1(\cdot)}$, we prove that for all small enough $\theta>0,$ there holds that $w_0\in A_{p_0(\cdot)},$ where the weight is determined by $w =…

We introduce an $L^p$-operator algebraic analogue of Hilbert C*- modules. We present the theory of concrete $L^p$-modules, their morphisms, and basic constructions including countable direct sums and tensor products. We then define…

The purpose of this note is to show in an accessible and self-contained way the existence of an isometric algebra embedding from $H^\infty(\D)$ into $L^\infty(\T)$, without appealing to Fatou's classical theorem on non-tangential limits of…

We study the predual of the space of functions of bounded variation defined over a metric measure space $({\rm X},{\sf d},\mathfrak m)$ with $\mathfrak m$ finite. More specifically, for any exponent $p\in(1,\infty)$ we construct an…