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Abstract: this article we explain the construction of nonorthogonal series expansions with respect to basis functions which are simple transforms of a single function. In mathematics such expansions are often called atomic decompositions, in terms of physics they are series expansions with respect to discrete sets of coherent states [22]. This means that all basis functions are derived from a single function by elementary operations such as shifts, modulations, scaling or rotations. An expansion of this... (Update)
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BibTeX entry: (Update)
@misc{ feichtinger-nonorthogonal,
author = "H. G. Feichtinger and K. Gröchenig",
title = "Non-Orthogonal Wavelet and Gabor Expansions, and Group Representations",
url = "citeseer.ist.psu.edu/683479.html" }
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57 A class of nonharmonic Fourier series (context) - Duffin, Schaeffer - 1952
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33 Ondelettes et bases hilbertiennes (context) - Lemarie, Meyer - 1986
28 Banach spaces related to integrable group representations an.. (context) - Feichtinger, Grochenig - 1989
28 Banach spaces related to integrable group representations an.. (context) - Feichtinger, Grochenig - 1989
10 Describing functions: atomic decompositions versus frames (context) - Grochenig
10 a new Segal algebra (context) - Feichtinger - 1981
7 Representation theorems for holomorphic and harmonic functio.. (context) - Coifman, Rochberg - 1980
3 Hankel forms and the Fock space (context) - Janson, Peetre et al. - 1987
2 Lattice size estimates for Gabor decompositions (context) - Walnut
2 Constructive Function Theory (context) - Feichtinger, of et al. - 1989
2 Function Spaces and Applications (context) - Feichtinger, Grochenig et al. - 1988
1 Function Spaces and Applications (context) - Frazier, Jawerth et al. - 1988
1 Unconditional bases in translation and dilation invariant fu.. (context) - Grochenig - 1987
1 CBMS-Lecture Notes (context) - Daubechies, Applications
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