Model spaces results for the Gabor and Wavelet transforms

Details Model spaces results for the Gabor and Wavelet transforms Model spaces results for the Gabor and Wavelet transforms

2008-04-21

arxiv.org/abs/0804.3254v1

Mathematics

Functional Analysis

Submitted to IEEE Transactions on Information Theory

Scientific paper

We prove that the unique Gabor atom with analytical model space is the
Gaussian function. We give an analogous result for the wavelet transform. For
the general case we give a new approach to study the irregular Gabor and
wavelet frames. We improve some results for Gabor atoms in the Feichtinger
algebra, and for a special class of wavelets.

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