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

A. Baranov, Y. Belov, A. Borichev, D. Yakubovich

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборникенаучнаярецензирование

Аннотация

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.
Язык оригиналаанглийский
Название основной публикацииRecent Trends in Analysis, Proceedings of the conferenece in honor of Nikolai Nikolski
ИздательTheta Foundation
ISBN (печатное издание)978-606-8443-02-7
СостояниеОпубликовано - 2013

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Baranov, A., Belov, Y., Borichev, A., & Yakubovich, D. (2013). Recent developments in spectral synthesis for exponential systems and for non-self-adjoint operators. В Recent Trends in Analysis, Proceedings of the conferenece in honor of Nikolai Nikolski Theta Foundation.