

Seminar on Complex Analysis (Gonchar Seminar)
May 14, 2012 18:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)






Spectral synthesis for exponential systems
A. D. Baranov^{} ^{} St. Petersburg State University, Department of Mathematics and Mechanics

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Abstract:
We consider the problem whether it is possible to recover an arbitrary function in $L^2$ from its generalized Fourier series with respect to some complete and minimal system of exponentials (it is known as the spectral
synthesis problem). The main result is as follows:
1. There exist complete and minimal systems of exponentials for which the spectral synthesis is not possible.
2. The spectral synthesis for exponential systems always holds up to a onedimensional defect.
We plan to discuss the idea of the proof of these results.
The talk is based on a joint work with Yurii Belov and Alexander Borichev.

