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Title: Deformations of bases and frames (with a focus on Gabor systems)
Abstract: Orthonormal bases are practical for many purposes, but they typically cease to be orthonormal bases once some kind of deformation is applied. On the other hand, there are many results in the literature on the stability of Riesz bases and frames under various notions of deformations and perturbations. I will discuss deformations of bases and frames with a focus on the case of Gabor systems, and show how results in this direction lead to obstructions to the existence of Gabor Riesz bases known as Balian–Low theorems. This talk is based on joint work with Mads Jakobsen, Franz Luef and Tron Omland.