Annihilating sets for the short time Fourier transform

• Autores: Carmen Fernández Rosell , Antonio Galbis Verdú
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 224, Nº 5, 2010, págs. 1904-1926
• Idioma: inglés
• DOI: 10.1016/j.aim.2010.01.010
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• Resumen

  • We obtain a class of subsets of R-2d such that the support of the short time Fourier transform (STFT) of a signal f is an element of L-2 (R-d) with respect to a window g is an element of L-2(R-d) cannot belong to this class unless f or g is identically zero. Moreover we prove that the L-2-norm of the STFT is essentially concentrated in the complement of such a set. A generalization to other Hilbert spaces of functions or distributions is also provided. To this aim we obtain some results on compactness of localization operators acting on weighted modulation Hilbert spaces

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