Model space results for the Gabor and wavelet transforms

Authors:
Gerard Ascensi;Joaquim Bruna
Affiliations:
Faculty of Mathematics, University of Vienna, Vienna, Austria;Departament de Matemàtiques, Universitat Autònoma de Barcelona, Cerdanyola del Vallès, Spain
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

We prove that the unique Gabor window leading to an analytic model space is the Gaussian one, and we give an analogous result for the wavelet transform. For the general case we give a new approach to study irregular Gabor and wavelet frames. We improve some known results for Gabor windows in the Feichtinger algebra, and for a special class of wavelets.