Quasi-Banach modulation spaces and localization operators on locally compact abelian groups

被引：3

作者：

Bastianoni, Federico ^{[1
]}

Cordero, Elena ^{[2
]}

机构：

[1] Politecn Co Torino, Dipartimento Sci Matemat, Corso Duca Abruzzi 24, I-10129 Turin, Italy

[2] Univ Torino, Dipartimento Matemat, Via Carlo Alberto 10, I-10123 Turin, Italy

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2022年 / 16卷 / 04期

关键词：

Time-frequency analysis; Locally compact abelian groups; Localization operators; Short-time Fourier transform; Quasi-Banach spaces; Modulation spaces; Wiener amalgam spaces; TIME-FREQUENCY ANALYSIS; PSEUDODIFFERENTIAL-OPERATORS; COHENS CLASS; DECOMPOSITION; DISTRIBUTIONS; CONTINUITY; CALCULUS; FRAMES;

D O I：

10.1007/s43037-022-00205-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce new quasi-Banach modulation spaces on locally compact abelian groups which coincide with the classical ones in the Banach setting and prove their main properties. Then, we study Gabor frames on quasi-lattices, significantly extending the original theory introduced by Grochenig and Strohmer. These issues are the key tools in showing boundedness results for Kohn-Nirenberg and localization operators on modulation spaces and studying their eigenfunctions' properties. In particular, the results in the Euclidean space are recaptured.

引用

页数：71

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[2] Publisher Correction: Quasi-Banach modulation spaces and localization operators on locally compact abelian groups
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