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arXiv · 1212.6014

Recent developments in spectral synthesis for exponential systems and for non-self-adjoint operators

Anton Baranov·Yurii Belov·Alexander Borichev·Dmitry Yakubovich
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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 $L^2(-\pi, \pi)$. 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.

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Anton Baranov, Yurii Belov, Alexander Borichev, Dmitry Yakubovich. 2012-12-25. Recent developments in spectral synthesis for exponential systems and for non-self-adjoint operators. https://arxiv.org/abs/1212.6014

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