Speaker: Stephen Casey (American University)

Title: Shannon Sampling via Poisson, Cauchy, Jacobi and Selberg


"The Poisson summation formula and Cauchy’s integral and residue formulas are two different aspects of a broad gauged duality formula which lies athwart most of analysis.'' S. Bochner

Our talk develops connections between some of the most powerful formulae in analysis - the Poisson summation formula, Cauchy’s integral and residue formulae, Jacobi interpolation, and the Selberg trace formula - to the Shannon sampling formula. These connections allow us to extend sampling in new directions, e.g., to unions of non-commensurate lattices, to the Riemann Sphere and to the Poincare disk. We close by discussing how to develop sampling for arbitrary Riemann surfaces using Ahlfors covering theory.

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