Sparse and redundant representation modeling of data assumes an ability to describe
signals as linear combinations of a few atoms from a pre-specified dictionary. As such, the …

Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those
parts of mathematics and its applications that use the struc ture of translations and …

Since its invention in 1979 the Feichtinger algebra has become a useful Banach space of
functions with applications in time-frequency analysis, the theory of pseudo-differential …

The modulation spaces Ms p, q (Rm), s∈ R, 1≤ p, q≤∞ to be discussed in this paper are
Banach spaces of tempered distributions σ on Rm, which are characterized by the behaviour …

The theory of reproducing kernels started with two papers of 1921 [449] and 1922 [45] which
dealt with typical reproducing kernels of Szegö and Bergman, and since then the theory has …

This authoritative text studies pseudodifferential and Fourier integral operators in the
framework of time-frequency analysis, providing an elementary approach, along with …

A notion of pseudoframes for subspaces (PFFS) is defined and characterized in a separable
Hilbert space H. PFFS functions in a manner of a frame for a subspace X in H. Yet none of …

This paper lays the foundation for a quantitative theory of Gabor expansionsf (x)=∑ k, nck,
ne2πinαxg (x− kβ). In analogy to wavelet expansions of Besov–Triebel–Lizorkin spaces, we …

This note provides historical perspective and background on the motivations which led to the
invention of the modulation spaces by the author almost 25 years ago, as well as comments …

Abstract The Density Theorem for Gabor Frames is one of the fundamental results of time-
frequency analysis. This expository survey attempts to reconstruct the long and very involved …