Gabor Windows and Dual Systems with Characterizations of Modulation Spaces of Localization Operators

Abstract

We show the sparse complete Gabor frame with systems over irregular lattices .The pairs of dual Gabor frame generated by compact support , desired frequency localization and polynomials are considered . Similarly we consider the Gabor windows supported on a closed interval and compactly supported dual windows with applied and computational harmonic analysis . We study the compactness of time – frequency analysis of localization operators on Hilbert space , partitions for the Gelfand triple and characterizations of modulation spaces with localization operators. We determine the Beurling density and shift-invariant weighted irregular Gabor systems , tight frames and dual systems using windows in the Schwartz class .