TY - CHAP

T1 - Recent developments in spectral synthesis for exponential systems and for non-self-adjoint operators

AU - Baranov, A.

AU - Belov, Y.

AU - Borichev, A.

AU - Yakubovich, D.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

M3 - Article in an anthology

SN - 978-606-8443-02-7

BT - Recent Trends in Analysis, Proceedings of the conferenece in honor of Nikolai Nikolski

PB - Theta Foundation

ER -