Foundations of Time-Frequency Analysis

By Karlheinz Gröchenig. Applied and Numerical Harmonic Analysis, 2000

1,631 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Civil and Structural Engineering, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/1a97ecaf1f067c44135fd3161a5c80a3497cb344

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Citations in the corpus

The Segal Algebra ${\bf S}_0({\Bbb R}^d)$ and Norm Summability of Fourier Series and Fourier Transforms (2006, background): “Furthermore, the embedding S0(R) ↪→ W (C, `1)(R) is dense and continuous and S0(R) ( W (C, `1)(R)∩F(W (C, `1)(R)) (see Feichtinger and Zimmermann [8], Losert [17] and Gröchenig [14]).”
The Faber–Krahn inequality for the short-time Fourier transform (2021, background): “Let S ′(R) be the space of temperate distributions and, for p ≥ 1, consider the subspace (called modulation space in the literature [34]) Mp(R) := { f ∈ S ′(R) : ‖ f ‖Mp := ‖V f ‖L p(R2) < ∞}.”
Generalized coorbit theory, Banach frames, and the relation to α‐modulation spaces (2008, background): “This situation coincides with the wellknown case of uniform Gabor frames [29].”
Banach Gelfand Triples for Gabor Analysis (2008, methodology): “which is sometimes called the fundamental identity of time-frequency analysis [29].”
Pseudodifferential operators on locally compact abelian groups and Sjöstrand's symbol class (2006, background): “We assume familiarity with Gabor frames and refer to [17], Ch.”
On the Probabilistic Cauchy Theory of the Cubic Nonlinear Schrödinger Equation on Rd, d≥3 (2014, neutral): “For this purpose, we first review some basic notions related to the so-called modulation spaces of time-frequency analysis [28].”
Frame properties of systems arising via iterated actions of operators (2019, neutral): “We refer to [10, 13, 6] and the references therein.”