相关论文: Banach frames for alpha-modulation spaces

The domain of definition of the divergence operator \delta on an abstract Wiener space (W, H, \mu) is extended to include W-valued and W\otimesW-valued "integrands". The main properties and characterizations of this extension are derived…

The residual amplitude modulation ($\mathrm{RAM}$) is the undesired, non-zero amplitude modulation that usually occurs when a phase modulation based on the electro-optic effect is imprinted on a laser beam. In this work, we show that…

We study families of time-frequency localization operators and derive a new characterization of modulation spaces. This characterization relates the size of the localization operators to the global time-frequency distribution. As a…

[L. Gavruta, Frames for Operators, Appl. comput. Harmon. Anal. 32(2012), 139-144] introduced a special kind of frames, named $K$-frames, where $K$ is an operator, in Hilbert spaces, is significant in frame theory and has many applications.…

The aim of this paper is to apply an extrapolation result without relying on convexification. We characterize ball Banach function spaces in terms of wavelets, formulated in a way that takes into account the smoothness properties of the…

We deduce continuity, compactness and invariance properties for quasi-Banach Orlicz modulation spaces. We characterize such spaces in terms of Gabor expansions and by their images under the Bargmann transform.

$\newcommand{mc}[1]{\mathcal{#1}}$ $\newcommand{D}{\mc{D}(\mc{Q},L^p,\ell_w^q)}$ We present a framework for the construction of structured, possibly compactly supported Banach frames and atomic decompositions for decomposition spaces. Such…

We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $(1+\varepsilon)$-isomorphic to…

We investigate mapping properties for the Bargmann transform on modulation spaces whose weights and their reciprocals are allowed to grow faster than exponentials. We prove that this transform is isometric and bijective from modulation…

Our aim in the current article is to extend the developments in Kruger, Ngai & Th\'era, SIAM J. Optim. 20(6), 3280-3296 (2010) and, more precisely, to characterize, in the Banach space setting, the stability of the local and global error…

We statistically analyse a recent sample of data points measuring the fine-structure constant alpha (relative to the terrestrial value) in quasar absorption systems. Using different statistical techniques, we find general agreement with…

We prove modulation invariant embedding bounds from Bochner spaces $L^p(\mathbb{W};X)$ on the Walsh group to outer-$L^p$ spaces on the Walsh extended phase plane. The Banach space $X$ is assumed to be UMD and sufficiently close to a Hilbert…

We study the invertibility of Banach algebras elements in their extensions, and invertible extensions of Banach and Hilbert space operators with prescribed growth conditions for the norm of inverses. As applications, the solutions of two…

Motivating the perturbations of frames in Hilbert and Banach spaces, in this paper we introduce the invariance of Fr\'echet frames under perturbation. Also we show that for any Fr\'echet spaces, there is a Fr\'echet frame and any element…

This paper is concerned with problems in the context of the theoretical foundation of adaptive (wavelet) algorithms for the numerical treatment of operator equations. It is well-known that the analysis of such schemes naturally leads to…

Reproducing kernel Hilbert spaces provide a foundational framework for kernel-based learning, where regularization and interpolation problems admit finite-dimensional solutions through classical representer theorems. Many modern learning…

In this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems. These include time-varying systems modeled with unbounded state-space operators acting…

We introduce new frames, called \textit{metaplectic Gabor frames}, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions. Namely, we develop the theory of metaplectic atoms in a full-general setting…

Gabor frames with Hermite functions are equivalent to sampling sequences in true Fock spaces of polyanalytic functions. In the L^2-case, such an equivalence follows from the unitarity of the polyanalytic Bargmann transform. We will…

We consider switched systems on Banach and Hilbert spaces governed by strongly continuous one-parameter semigroups of linear evolution operators. We provide necessary and sufficient conditions for their global exponential stability, uniform…