Recent developments in spectral synthesis for exponential systems and for non-self-adjoint operators
Functional Analysis
2016-04-21 v1 Complex Variables
Spectral Theory
Abstract
We survey recent results concerning the hereditary completeness of some special systems of functions and the spectral synthesis problem for a related class of linear operators. We present a solution of the spectral synthesis problem for systems of exponentials in . Analogous results are obtained for the systems of reproducing kernels in the de Branges spaces of entire functions. We also apply these results (via a functional model) to the spectral theory of rank one perturbations of compact self-adjoint operators.
Cite
@article{arxiv.1212.6014,
title = {Recent developments in spectral synthesis for exponential systems and for non-self-adjoint operators},
author = {Anton Baranov and Yurii Belov and Alexander Borichev and Dmitry Yakubovich},
journal= {arXiv preprint arXiv:1212.6014},
year = {2016}
}
Comments
This is survey of some recent results by the authors (including arXiv:1112.5551). The paper is to appear in the Proceeding of the conference "Recent Trends in Analysis" (Bordeaux, 31.08.2011-02.09.2011) in honor of Nikolai Nikolski