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

DOI10.1007/s43670-024-00085-xzbMATH Open1542.42034MaRDI QIDQ6564357

Elena Cordero, Gianluca Giacchi

Publication date: 1 July 2024

Published in: Sampling Theory, Signal Processing, and Data Analysis (Search for Journal in Brave)

zbMATH Keywords

symplectic groupframesmodulation spacestime-frequency analysismetaplectic groupWiener amalgam spacestime-frequency representations

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Function spaces arising in harmonic analysis (42B35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) General harmonic expansions, frames (42C15)

Cites Work

• Unnamed Item
• Modulation spaces \(M^{p,q}\) for \(0<p,q\leq\infty\)
• Time-frequency analysis on modulation spaces \(M_{m}^{p,q}\), \(0 < p,q \leqslant \infty\).
• Pseudodifferential operators on ultra-modulation spaces.
• Foundations of time-frequency analysis
• Uncertainty principle of complex-valued functions in specific free metaplectic transformation domains
• Wigner analysis of operators. I: Pseudodifferential operators and wave fronts
• On foundational discretization barriers in STFT phase retrieval
• Time-frequency analysis of operators
• Strichartz estimates for the metaplectic representation
• Characterization of modulation spaces by symplectic representations and applications to Schrödinger equations
• Generalized Amalgams, With Applications to Fourier Transform
• Symplectic Methods in Harmonic Analysis and in Mathematical Physics
• Harmonic Analysis in Phase Space. (AM-122)
• Modulation Spaces
• Symplectic analysis of time-frequency spaces
• The metaplectic action on modulation spaces
• Metaplectic Gabor frames and symplectic analysis of time-frequency spaces

Related Items (3)

Convolution based fractional Wigner distribution and ambiguity function: theory and applications ⋮ Boundedness of metaplectic operators within \(L^p\) spaces, applications to pseudodifferential calculus, and time-frequency representations ⋮ Extending the scaling Wigner distribution in the realm of linear canonical domains

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