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43

Sep 23, 2013
09/13

by
Anton Baranov; Yurii Belov; Alexander Borichev; Dmitry Yakubovich

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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...

Source: http://arxiv.org/abs/1212.6014v1

45
45

Sep 24, 2013
09/13

by
Yuri Bilu; Alexander Borichev

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We obtain a fully explicit quantitative version of the Eisenstein theorem on algebraic power series which is more suitable for certain applications than the existing version due to Dwork, Robba, Schmidt and van der Poorten. We also treat ramified series and Laurent series, and we demonstrate some applications; for instance, we estimate the discriminant of the number field generated by the coefficients.

Source: http://arxiv.org/abs/1112.2290v2

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4.0

Jun 28, 2018
06/18

by
Anton Baranov; Yurii Belov; Alexander Borichev

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We describe the radial Fock type spaces which possess Riesz bases of normalized reproducing kernels and which are (are not) isomorphic to de Branges spaces in terms of the weight functions.

Topics: Functional Analysis, Complex Variables, Mathematics

Source: http://arxiv.org/abs/1512.09001