We provide a comprehensive overview of the theoretical framework surrounding modulation spaces and their characterizations, particularly focusing on the role of metaplectic operators and time-frequency representations. We highlight the metaplectic action which is hidden in their construction and guarantees equivalent (quasi-)norms for such spaces. In particular, this work provides new characterizations via the sub- manifold of shift-invertible symplectic matrices. Similar results hold for the Wiener amalgam spaces.

Cordero, E. (2024). Excursus on modulation spaces via metaplectic operators and related time-frequency representations. SAMPLING THEORY, SIGNAL PROCESSING, AND DATA ANALYSIS, 22(1), 1-18 [10.1007/s43670-024-00085-x].

Excursus on modulation spaces via metaplectic operators and related time-frequency representations

Giacchi Gianluca
2024

Abstract

We provide a comprehensive overview of the theoretical framework surrounding modulation spaces and their characterizations, particularly focusing on the role of metaplectic operators and time-frequency representations. We highlight the metaplectic action which is hidden in their construction and guarantees equivalent (quasi-)norms for such spaces. In particular, this work provides new characterizations via the sub- manifold of shift-invertible symplectic matrices. Similar results hold for the Wiener amalgam spaces.
2024
Cordero, E. (2024). Excursus on modulation spaces via metaplectic operators and related time-frequency representations. SAMPLING THEORY, SIGNAL PROCESSING, AND DATA ANALYSIS, 22(1), 1-18 [10.1007/s43670-024-00085-x].
Cordero, Elena, Giacchi, Gianluca
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/966733
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