**Speaker:** Stephen Casey (American University)

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

**Abstract: **

"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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