Excursus on modulation spaces via metaplectic operators and related time-frequency representations
Copyright policy )Excursus on modulation spaces via metaplectic operators and related time-frequency representations
AbstractWe 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 submanifold of shift-invertible symplectic matrices. Similar results hold for the Wiener amalgam spaces.
- Alma Mater Studiorum University of Bologna Italy
- The Sense Innovation and Research Center Switzerland
- University of Lausanne Switzerland
- University Hospital of Lausanne Switzerland
- University of Turin Italy
Wiener amalgam spaces, Frames Time-frequency analysis Modulation spaces Wiener amalgam spaces Time-frequency representations Metaplectic group Symplectic group, metaplectic group, General harmonic expansions, frames, Determinants, permanents, traces, other special matrix functions, time-frequency analysis, Mathematics - Analysis of PDEs, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, frames, FOS: Mathematics, Frames; Time-frequency analysis; Modulation spaces; Wiener amalgam spaces; Time-frequency representations; Metaplectic group; Symplectic group, 42C15, 42B35, 42A38, time-frequency representations, Function spaces arising in harmonic analysis, symplectic group, modulation spaces, Analysis of PDEs (math.AP)
Wiener amalgam spaces, Frames Time-frequency analysis Modulation spaces Wiener amalgam spaces Time-frequency representations Metaplectic group Symplectic group, metaplectic group, General harmonic expansions, frames, Determinants, permanents, traces, other special matrix functions, time-frequency analysis, Mathematics - Analysis of PDEs, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, frames, FOS: Mathematics, Frames; Time-frequency analysis; Modulation spaces; Wiener amalgam spaces; Time-frequency representations; Metaplectic group; Symplectic group, 42C15, 42B35, 42A38, time-frequency representations, Function spaces arising in harmonic analysis, symplectic group, modulation spaces, Analysis of PDEs (math.AP)
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