Variable bandwidth and sampling theorems

Abstract: We study sampling theorems in spectral subspaces of a uniformly elliptic differential operator. For constant coefficients, these are spaces of bandlimited functions, whereas for general elliptic operators, the resulting spaces consist of functions of "variable bandwidth". This is one of several constructions that gives meaning to the intuitive notion of a local and time-varying bandwidth. The interpretation is supported by the results on sampling theorems and necessary sampling density.

classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory

Audience: researchers in the topic

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