Balian-Low Type Results for Gabor Schauder Bases

Abstract

The uncertainty principle implies that a function and its Fourier transform cannot both be well-localized. The Balian-Low theorem is a version of the uncertainty principle for generators of Gabor orthonormal bases. This dissertation proves a new Balian-Low type theorem for compactly supported generators of Gabor Schauder bases. Moreover, we show that the classical Balian-Low theorem for orthonormal bases does not hold for Schauder bases.