Search results for "Localization operator"

showing 2 items of 2 documents

Compactness of time-frequency localization operators on L2(Rd)

2006

Abstract In this paper, we consider localization operators on L 2 ( R d ) defined by symbols in a subclass of the modulation space M ∞ ( R 2 d ) . We show that these operators are compact and that this subclass is “optimal” for compactness.

Discrete mathematicsModulation spaceCompact operatorApproximation propertyShort-time Fourier transformModulation spaceLocalization operatorOperator theoryCompact operatorCompact operator on Hilbert spaceSubclassCompact spaceTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESShort-time Fourier transformAnalysisComputer Science::Formal Languages and Automata TheoryMathematicsJournal of Functional Analysis
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Annihilating sets for the short time Fourier transform

2010

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.

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