Vector-Valued Gabor Frames and Deformation of Gabor Systems with Gabor Orthonormal Bases

Abstract

The description of the spectra tiling properties and Gabor orthonormal bases generated by the unit cubes and of the exponential for the 𝑛-cube are characterized. In addition the uniformity of non-uniform Gabor bases, atomic characterizations of modulation spaces through Gabor representations with Weyl-Heisenberg frames on Hilbert space, slanted matrices and Banach frames are clearly improved. We obtain the density, stability, generated characteristic function and Hamiltonian deformations of Gabor frames. We find estimates for vector –valued Gabor frames of Hermite functions plus periodic subsets of the real line. The Gabor frame sets for subspace with totally positive functions and deformation of Gabor systems are considered.