Balint Farkas: An extremal problem from harmonic analysis at the intersection of functional analysis and linear programming

Abstract: The Delsarte extremal problem seeks the maximization of the integral of a real positive definite function subject to a sign constraint and a normalization condition. The problem is of interest because of its many connections to packings, tilings, and other geometric or combinatorial problems, providing effective bounds. In this talk, we describe the linear programming dual of the Delsarte problem over the Wiener algebra of a locally compact Abelian group, and prove strong duality via tools from functional analysis. The talk reports on a joint work with E. Berdysheva, M. Gaál, M. Ramabulana, and Sz. Révész.

The talk will be live and streamed.

Roman Drnovšek and Daniel Smertnig