A Hilbert C*-module for Gabor systems

Details A Hilbert C*-module for Gabor systems A Hilbert C*-module for Gabor systems

2001-02-20

arxiv.org/abs/math/0102165v1

Mathematics

Functional Analysis

12 pages

Scientific paper

We construct Hilbert $C^*$-modules useful for studying Gabor systems and show that they are Banach algebras under pointwise multiplication. For rational $ab<1$ we prove that the set of functions $g \in L^2(R)$ so that $(g,a,b)$ is a Bessel system is an ideal for the Hilbert $C^*$-module given this pointwise algebraic structure. This allows us to give a multiplicative perturbation theorem for frames. Finally we show that a system $(g,a,b)$ yields a frame for $L^2(R)$ iff it is a modular frame for the given Hilbert $C^*$-module.

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