Interpolation formulas and extremal problems in Fourier analysis

by Prof. Danylo Radchenko (University of Lille)

Wednesday May 14, 2025, 1:00 PM → 2:00 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

A Fourier interpolation formula is an identity allowing one to reconstruct a function from discrete samples of it and its Fourier transform. Although many such identities are classical and well-known for band-limited functions, first general Fourier interpolation formulas were constructed only recently, motivated by questions arising from the sphere packing problem.

I will discuss the recent constructions of Fourier interpolation formulas based on modular forms and explain the role that similar formulas are expected to play in sphere packing and energy minimization problems. I will also describe the recent solution of the Hörmander-Bernhardsson extremal problem, and some remarkable properties of the Hörmander-Bernhardsson function.