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Regular version of the site

Article

Hereditary completeness for systems of exponentials and reproducing kernels

Advances in Mathematics. 2013. Vol. 235. P. 525-554.
Baranov A., Belov Y., Borichev A.

We solve the spectral synthesis problem for exponential systems on an interval. Namely, we prove that any complete and minimal system of exponentials in L^2(-a,a) is hereditarily complete up to a one-dimensional defect. However, this one-dimensional defect is possible and, thus, there exist nonhereditarily complete exponential systems. Analogous results are obtained for systems
of reproducing kernels in de Branges spaces. For a wide class of de Branges spaces we construct nonhereditarily complete systems of reproducing kernels, thus answering a question posed by N. Nikolski.