DUAL PAIRS OF GABOR FRAMES FOR TRIGONOMETRIC GENERATORS WITHOUT THE PARTITION OF UNITY PROPERTY

Abstract

Frames is a strong tool to obtain series expansions in Hilbert spaces under less restrictive conditions than imposed by orthonormal bases. In order to apply frame theory it is necessary to construct a pair of so called dual frames. The goal of the article is to provide explicit constructions of dual pairs of frames having Gabor structure. Unlike the results presented in the literature we do not base the constructions on a generator satisfying the partition of unity constraint.