A Hilbert C*-module for Gabor systems

الأصل · EN

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 ∈ L²(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 L²(R) iff it is a modular frame for the given Hilbert C*-module.