Approximation by linear combinations of translates in invariant Banach spaces of tempered distributions via Tauberian conditions

DOI10.1016/j.jat.2023.105908zbMath1526.43002OpenAlexW4367669901MaRDI QIDQ6156881

Anupam Gumber, Hans G. Feichtinger

Publication date: 19 June 2023

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2023.105908

zbMATH Keywords

Banach modulesmodulation spacesTauberian theoremsBeurling algebraweighted amalgam spacesBanach spaces of tempered distributionsapproximation by translations

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Compactness in Banach (or normed) spaces (46B50) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Topological linear spaces of test functions, distributions and ultradistributions (46F05) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Ordered topological linear spaces, vector lattices (46A40) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25) Tauberian theorems (40E05) Measure algebras on groups, semigroups, etc. (43A10)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• New distribution spaces associated to translation-invariant Banach spaces
• Banach spaces related to integrable group representations and their atomic decompositions. I
• On pseudodifferential operators with symbols in generalized Shubin classes and an application to Landau-Weyl operators
• Harmonic analysis based on certain commutative Banach algebras
• Compactness in translation invariant Banach spaces of distributions and compact multipliers
• Banach spaces of distributions having two module structures
• On a new Segal algebra
• Foundations of time-frequency analysis
• Spaces of test functions via the STFT
• Schatten properties, nuclearity and minimality of phase shift invariant spaces
• Time-frequency analysis of operators
• On the completeness of Gaussians in a Hilbert functional space
• Translation-modulation invariant Banach spaces of ultradistributions
• Groupes localement isomorphes et transformation de Fourier avec poids
• Generalized Amalgams, With Applications to Fourier Transform
• Banach Spaces of Distributions Defined by Decomposition Methods, I
• A Characterization of Minimal Homogeneous Banach Spaces
• Segal Algebras and Left Normed Ideals
• Results on Banach ideals and spaces of multipliers.
• A Novel Mathematical Approach to the Theory of Translation Invariant Linear Systems
• Embeddings and compactness for generalized Sobolev–Shubin spaces and modulation spaces
• Tauberian Theory
• Translation and modulation invariant Banach spaces of tempered distributions satisfy the metric approximation property
• Completeness of shifted dilates in invariant Banach spaces of tempered distributions
• Modulation Spaces
• Distribution Proof of Wiener's Tauberian Theorem
• Choosing Function Spaces in Harmonic Analysis
• Multipliers and tensor products of $L^{p}$-spaces of locally compact groups
• Closed Ideals in Subalgebras of Banach Algebras. I
• Shorter Notes: Local Units in L 1 (G)

This page was built for publication: Approximation by linear combinations of translates in invariant Banach spaces of tempered distributions via Tauberian conditions