泛函分析
In this paper, we establish a suitable version of the Hahn-Banach theorem within the framework of Colombeau spaces, a class of spaces used to model generalized functions. Our approach addresses the case where maps are defined…
We consider the class of weakly porous sets in Euclidean spaces. As our main goal, we give a precise characterization in terms of dyadic covering of these sets. Also, we obtain the Carleson embedding inequality for porous sets.
Generalized Ces\`aro operators $C_t$, for $t\in [0,1)$, are investigated when they act on the disc algebra $A(\mathbb{D})$ and on the Hardy spaces $H^p$, for $1\leq p \leq \infty$. We study the continuity, compactness, spectrum and point…
We develop a notion of capacity for the Drury-Arveson space $H^2_d$ of holomorphic functions on the Euclidean unit ball. We show that every function in $H^2_d$ has a non-tangential limit (in fact Kor\'anyi limit) at every point in the…
In this paper, we study Hausdorff operator $\mathcal{H}_\mu$ on a large class of weighted mixed norm Fock spaces $F_\phi^{p,q}$ for $1\leq p,q\leq\infty$. The boundedness and compactness of $\mathcal{H}_\mu$ on $F_\phi^{p,q}$ are…
A sequence $\{\delta_n^{(k)}\}$ associated to a Bochner differential operator is introduced as an effective tool to study this kind of operators. Some properties of this sequence are proven and used to deduce that a particular operator…
For the Weyl-Heisenberg group, convolutions between functions and operators were defined by Werner as a part of a framework called quantum harmonic analysis. We show how recent results by Feichtinger can be used to extend this definition to…
We study $\ell^r$-valued extensions of linear operators defined on Lebesgue spaces with variable exponent. Under some natural (and usual) conditions on the exponents, we characterize $1\leq r\leq \infty$ such that every bounded linear…
In this paper we prove that the Anzellotti pairing can be regarded as a relaxed functional with respect to the weak* convergence in the space BV of functions of bounded variation. The crucial tool is a preliminary integral representation of…
In this paper, we study the basic properties of Toeplitz Operators with positive measures $\mu$ on harmonic Fock spaces. We prove equivalent conditions for boundedness, compactness and Schatten classes $S_{p}$ of $T_{\mu}$ by using the…
This note gives a summary of ideas concerning Applied Fourier Analysis, mostly formulated for those who have to give such courses to engineers or mathematicians interested in real life applications. It tries to answer recurrent questions…
Consider a group $G$ of order $M$ acting unitarily on a real inner product space $V$. We show that the sorting based embedding obtained by applying a general linear map $\alpha : \mathbb{R}^{M \times N} \to \mathbb{R}^D$ to the invariant…
It is the purpose of this article to compare various concepts of ``function spaces''. In particular we compare notions of the concept of Banach Function Spaces (in the spirit of Luxemburg-Zaanen) to the setting of solid BF-spaces as it is…
In this paper, we discuss k-quasi-m-isometric composition operators and weighted composition operators on directed graphs with one circuit and more than one branching vertex.
Motivated by the barycenter problem in optimal transportation theory, Kolesnikov--Werner recently extended the notion of the Legendre duality relation for two functions to the case for multiple functions. We further generalize the duality…
We study the fundamental properties of pointwise semi-Lipschitz functions between asymmetric spaces, which are the natural asymmetric counterpart of pointwise Lipschitz functions. We also study the influence that partial symmetries of a…
We develop the quantum harmonic analysis framework in the reducible setting and apply our findings to polyanalytic Fock spaces. In particular, we explain some phenomena observed in arXiv:2201.10230 and answer a few related open questions.…
We determine the asymptotics of the block Toeplitz determinants $\det T_n(\phi)$ as $n\to\infty$ for $N\times N$ matrix-valued piecewise continuous functions $\phi$ with a finitely many jumps under mild additional conditions. In particular,…
In this paper, we introduce and study the Weyl transform of functions which are integrable with respect to a vector measure on a phase space associated to a locally compact abelian group. We also study the Weyl transform of vector measures.…
In this article, we study the ccs-Daugavet, ccs-$\Delta$, super-Daugavet, super-$\Delta$, Daugavet, $\Delta$, and $\nabla$ points in the unit balls of vector-valued function spaces $C_0(L, X)$, $A(K, X)$, $L_\infty(\mu, X)$, and $L_1(\mu,…