Abstract:
We consider the problem whether it is possible to recover an arbitrary function in L2 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 one-dimensional 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.