泛函分析

We investigate the uniqueness of short-time Fourier transform phase retrieval problems in $L^2(\mathbb{R})$. In particular, for underlying window functions whose Fourier transform decay faster than any exponential function, we derive…

In this paper we study best \(m\)-term trigonometric approximation in weighted Wiener spaces and its consequences for Besov and Sobolev spaces with bounded mixed derivative/difference. We obtain several sharp asymptotic bounds for weighted…

In this paper, by introducing some parameters, we define and study certain $p$-adic Hardy-Littlewood-P\'{o}lya-type integral operators acting on $p$-adic weighted Lebesgue spaces. We completely characterize $L^{q}-L^{r}$ boundedness of…

We provide a general framework for no-arbitrage concepts in topological vector lattices, which covers many of the well-known no-arbitrage concepts as particular cases. The main structural condition we impose is that the outcomes of trading…

Let $A\colon H\rightarrow H$ be a normal operator on an infinite-dimensional separable Hilbert space $H$ and let $S\subseteq H$ be a finite subset such that $\{A^nx\}_{n\geq 0,\,x\in S}$ can be rescaled to form a frame for $H$. That is,…

Tchakaloff's theorem from 1957 asserts the existence of exact quadrature rules with non-negative weights for any polynomial space of finite degree on $\mathbb{R}^d$ if the underlying measure is positive, compactly supported, and absolutely…

In this article we develop the direct and inverse scattering theory of the Ablowitz-Kaup-Newell-Segur (AKNS) system $\bv_x=(ik\zS+\CQ(x))\bv$, where $\zS$ is a diagonal $n\times n$ matrix with diagonal entries $1$ and $-1$ and a single zero…

We study fractal sets $\Gamma\subset \mathbb{R}^n$ with non-empty interior $\Omega$, that are attractors of iterated function systems (IFSs) of contracting similarities satisfying the open set condition. Examples for $n=2$ are the closures…

In this paper, we study three types of Birkhoff-James orthogonality in Hilbert $C^*$-modules, that is, the strong, quasi-strong, and original Birkhoff-James orthogonality. In general, the strong Birkhoff-James orthogonality is stronger than…

This paper investigates the eigenvalue problem of integral operators whose kernels can be expressed as a finite sum of pairwise products of single-variable functions, making them separable. By consdiering the matrix form of the separable…

We establish weighted weak-type bounds for the Bergman projection with respect to Bekoll\'e-Bonami characteristics. We present two proofs of an improved quantitative weak-type $(1,1)$ estimate, as well as sharp weak-type $(p,p)$ bounds for…

We intend to study the uniqueness of the Hahn-Banach extensions of linear functionals on a subspace in locally convex spaces. Various characterizations are derived when a subspace $Y$ has an analogous version of property-U (introduced by…

Let $E_1, \ldots, E_m$ be (non necessarily Archimedean) Riesz spaces, let $F$ be an Archimedean Riesz space and let $A \colon E_1 \times \cdots \times E_m \to F$ be a regular disjointness preserving $m$-linear operator. We prove that all…

We give an elementary proof of the folklore result that the Agler norm of a function is determined by its norm on commuting tuples of nilpotent matrices. The proof is variation on a standard cone separation argument. The topic is closely…

Recently, two new topological properties for operators acting on a topological vector space were introduced: strong hypercyclicity and hypermixing. We introduce a new property called ultra hypercyclicity and compare it to strong…

Given $n\in\mathbb{N}$ any point on the closed unit disk $\overline{\mathbb{D}}$ can be written as the average of $n$ points on the unit circle $\mathbb{S}^1$. Here we discuss a non-commutative version of this result. We prove that for any…

In this note, we develop a parallel theory of the classical Sz.-Nagy--Foias dilation and model theory for a single contraction operator in the setting of pairs of \em{{$q$-commuting}} contraction operators for a unimodular complex number…

In this paper we are interested to connect Koopman semigroups in Lebesgue funcion spaces $L^p(\R^+)$ and $C_0$-semigroups in Lebesgue sequence spaces $\ell^p$ for $1\le p < \infty$. To get this we use certain Poisson transformation ${\P}:…

We propose two interrelated advances in the theory of adjointable operators on Hilbert C*-modules. First, we give a set of equivalent, verifiable conditions characterizing positivity of general $n\times n$ block operator matrices acting on…

The classical Littlewood's theorem establishes boundedness and provides a norm estimate for composition operators on the Hardy space. In this paper, we offer an alternative proof of boundedness and derive a new norm estimate that improves…