泛函分析

We present and study some transfinite versions of (almost isometric) ideals in Banach spaces. As these notions are closely related with Lindenstrauss and Gurari\u{\i} spaces respectively, we will present a similar characterization for…

We establish that the Fourier transform $\mathcal{F}: L^p(\mathbb{R}^d)\to L^{p',p}(\mathbb{R}^d)$, for $d\in\mathbb{N}$ and $1<p<2$, is not strictly singular, thereby confirming the optimality of the source and target spaces. A~similar…

We study the behaviour of functions of dissipative operators under relatively bounded and relatively trace class perturbation. We introduce and study the class of analytic relatively operator Lipschitz functions. An essential role is played…

We define the harmonic Bergman space on locally finite trees with respect to a suitable probabilistic Laplacian and a class of weighted flow measures. We characterise the corresponding Bergman projection and prove that it is bounded on…

Let $n\geqslant 3$ be an integer. For the Bekoll\'e-Bonami weight $\omega$ on the real unit ball $\mathbb{B}_n$, we obtain the following sharp one-weight estimate for the $\mathcal{H}$-harmonic Bergman projection: for $1<p<\infty$ and…

Let $K$ be a compact subgroup of a locally compact group $G$. We investigate a Pompeiu type problem for homogeneous spaces $G/K$. Suppose $E$ is a compact subset of $G/K$. Using recent work of L\'{a}szl\'{o} Sz\'{e}kelyhidi on $K$-spectral…

Given a map $f \colon E \longrightarrow F$ between Banach spaces (or Banach lattices), a set $A$ of $E$-valued bounded sequences, ${\bf x} \in A$ and a vector topology $\tau$ on $F$, we investigate the existence of an infinite dimensional…

In this paper, we survey and refine several results -- some previously established in the literature -- that facilitate the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We apply…

Sampled Gabor phase retrieval - the problem of recovering a square-integrable signal from the magnitude of its Gabor transform sampled on a lattice - is a fundamental problem in signal processing, with important applications in areas such…

Gabor phase retrieval is the problem of reconstructing a signal from only the magnitudes of its Gabor transform. Previous findings suggest a possible link between unique solvability of the discrete problem (recovery from measurements on a…

The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…

Continuous spectrum operators (CSOs), characterized by spectra comprising continuous intervals rather than discrete eigenvalues, are pivotal in quantum mechanics, wave propagation, and systems governed by partial differential equations.…

In this article, using growth functions we introduce generalized matrix-weighted Besov-Triebel-Lizorkin-type spaces with matrix $\mathcal{A}_{\infty}$ weights. We first characterize these spaces, respectively, in terms of the…

In this study, multivalued generalizations of certain classes of single-valued transformations defined on metric spaces are obtained. Building upon recently introduced concepts such as mappings contracting perimeters of triangles, new…

In this paper, we give a decomposition of the gradient measure $Du$ of an arbitrary function of bounded variation $u$ into a sum of atoms $\mu=D\chi_{F}$, where $F$ is a set of finite perimeter. The atoms further satisfy the support,…

In this paper we obtain a complete characterization of reducing, invariant, and hyperinvariant subspaces for the completely non-unitary component of a power partial isometry. In particular, precise characterization of reducing, invariant,…

In the spirit of the ground-breaking result of Bourgain--Brezis--Mironescu, we establish some characterizations of Sobolev functions in metric measure spaces including fractals like the Vicsek set, the Sierpi\'{n}ski gasket and the…

In this paper, $\mathcal{G}(g,L,M,N)$ denotes a $L-$window Gabor system on a periodic set $\mathbb{S}$, where $L,M,M\in \mathbb{N}$ and $g=\{g_l\}_{l\in \mathbb{N}_L}\subset \ell^2(\mathbb{S})$. We characterize which $g$ generates a…

We study the determination of functions in Fock space from samples of their absolute value, known as the phase retrieval problem in Fock space. An important finding in this research field asserts that phaseless sampling on lattices of…

Due to its appearance in a remarkably wide field of applications, such as audio processing and coherent diffraction imaging, the short-time Fourier transform (STFT) phase retrieval problem has seen a great deal of attention in recent years.…