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Recent developments in spectral synthesis for exponential systems and for non-self-adjoint operators (1212.6014v1)
Published 25 Dec 2012 in math.FA, math.CV, and math.SP
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 $L2(-\pi, \pi)$. 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.