6533b870fe1ef96bd12cf28d

RESEARCH PRODUCT

Annihilating sets for the short time Fourier transform

Antonio GalbisCarmen Fernández

subject

Mathematics(all)Modulation spacePure mathematicsLocalization operatorsUncertainty principleGeneral MathematicsMathematical analysisShort-time Fourier transformHilbert spaceHilbert spectral analysissymbols.namesakeModulation spacesCompact spaceNorm (mathematics)Uncertainty principlesymbolsAnnihilating setsShort time Fourier transformMathematics

description

Abstract We obtain a class of subsets of R 2 d such that the support of the short time Fourier transform (STFT) of a signal f ∈ L 2 ( R d ) with respect to a window g ∈ 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.

yearjournalcountryeditionlanguage
2010-08-01Advances in Mathematics
10.1016/j.aim.2010.01.010http://dx.doi.org/10.1016/j.aim.2010.01.010