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.
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页数：71
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