Inversion formulas for the short-time Fourier transform

DOI10.1007/BF02922064zbMath1101.42012OpenAlexW2075243362MaRDI QIDQ2434072

Ferenc Weisz, Hans G. Feichtinger

Publication date: 31 October 2006

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02922064

zbMATH Keywords

Herz spacesshort-time Fourier transformWiener amalgam spaces\(\theta\)-summabilitytransform time-frequency analysis

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Function spaces arising in harmonic analysis (42B35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) General harmonic expansions, frames (42C15) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Summability in several variables (42B08)

Related Items

Navier-Stokes equation in super-critical spaces \(E_{p,q}^s\) ⋮ Convergence of wavelet frame operators as the sampling density tends to infinity ⋮ Inversion formula for the windowed Fourier transform. II ⋮ Inversion formulas for the continuous wavelet transform ⋮ Summability of Gabor expansions and Hardy spaces ⋮ Convergence of Riemannian sums of inverse wavelet transforms ⋮ Inversion of the wavelet transform using Riemannian sums ⋮ Pointwise summability of Gabor expansions ⋮ Asymptotic properties of Gabor frame operators as sampling density tends to infinity ⋮ Paley-Wiener theorems and uncertainty principles for the windowed linear canonical transform ⋮ Summability of Fourier transforms on mixed-norm Lebesgue spaces via associated Herz spaces

Cites Work

• Foundations of time-frequency analysis
• The Segal algebra \(\mathbf S_0(\mathbb R^d)\) and norm summability of Fourier series and Fourier transforms
• On convergence and growth of partial sums of Fourier series
• Gabor meets Littlewood–Paley: Gabor expansions in L^p(R^d)
• A Theory of Hardy Spaces Associated to the Herz Spaces
• Continuous and Discrete Wavelet Transforms
• Summability of Multi-Dimensional Fourier Series and Hardy Spaces
• Wiener amalgams and pointwise summability of Fourier transforms and Fourier series
• On the convergence of multiple Fourier series
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