Seminar: Discrete uniqueness pairs for the Fourier transform
Didier Pilod, Professor @ Department of Mathematics, University of Bergen
Abstract:
A pair (M,N) of sets of R is called a uniqueness pair for the Fourier transform if f=0 on M and F(f)=0 on N implies that f=0 on R. Here F(f) denotes the Fourier transform of and R are the real numbers.
In this talk I will go through a recent work of Kulikov, Nazarov and Sodin, in which the authors give sufficient conditions for a pair of discrete sets of R to be a uniqueness pair for the Fourier transform.
Their result extends former results of Radchenko and Viazovska, and Ramos and Souza. The proof combines in an elegant way Fourier analysis and complex analysis.
The article on which I will base my talk is the following:
"Fourier Uniqueness and Non-Uniqueness Pairs" by Aleksei Kulikov, Fedor Nazarov and Mikhail Sodin, Journal of Mathematical Physics, Analysis, Geometry, 21 (2025), no 1, 84-130.