Avdonin's theorem constitutes a seminal finding in the study of Riesz bases of exponentials, and is extensively used also in recent contributions to the problem. The primary objective of this talk is to deliver a comprehensive and self-contained proof of Avdonin's theorem. Moreover, various corollaries stemming from Avdonin's theorem will be discussed, including results by Levin, Golovin, Katsnelson, and Kadec.
Reference: S. A. Avdonin, On the question of Riesz bases of exponential functions in L^2, Vestnik Leningrad Univ. Math. 7 (1979).
This is the first part of a presentation on this topic.