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Majorization in de Branges spaces I. Representability of subspaces
Journal of Functional Analysis. 2010. No. 8. P. 2601-2636.
Baranov A., Woracek H.
Baranov A., Belov Y., Borichev A., Advances in Mathematics 2013 Vol. 235 P. 525-554
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 ...
Added: February 27, 2014
Shirokov N. A., Rozenblum G., CUBO A mathematical Journal 2010 No. 1 P. 117-134
Added: January 18, 2014
Baranov A., Yakubovich D., Advances in Mathematics 2016 Vol. 302 P. 740-798
We study spectral properties of nonselfadjoint rank one perturbations of compact selfadjoint operators. The problems under consideration include completeness of eigenvectors, relations between completeness of the perturbed operator and its adjoint, and the spectral synthesis problem. We obtain new criteria for completeness and spectral synthesis in this class as well as a series of counterexamples ...
Added: February 25, 2018
Baranov A., Belov Y., Borichev A., Geometric and Functional Analysis 2015 Vol. 25 No. 2 P. 417-452
We solve completely the spectral synthesis problem for reproducing kernels in the de Branges spaces H(E). Namely, we describe the de Branges spaces H(E) such that every complete and minimal system of reproducing kernels {kλ}λ∈Λ with complete biorthogonal {gλ}λ∈Λ admits the spectral synthesis, i.e., f∈Span¯{(f,gλ)kλ:λ∈Λ} for any f in $${\mathcal{H}(E)}$$H(E). Surprisingly, this property takes place ...
Added: October 7, 2015
Gladkaya A., Виноградов О. Л., St Petersburg Mathematical Journal 2015 Vol. 26 P. 867-879
Results of Chebyshev and Bernstein about polynomials with the smallest deviation from zero in a weighted norm are extended to entire functions of exponential type. Suppose that a function \rho_m belongs to the Cartwright class, is of type m, and is positive on the real axis. Let \sigma\geqslant m. Functions that have the smallest deviation ...
Added: January 28, 2019
Abakumov E., Baranov A., Belov Y., International Mathematics Research Notices 2015 No. 15 P. 6699-6733
We study the localization of zeros for Cauchy transforms of discrete measures on the real line. This question is motivated by the theory of canonical systems of differential equations. In particular, we prove that the spaces of Cauchy transforms having the localization property are in one-to-one correspondence with the canonical systems of special type, namely, ...
Added: October 7, 2015
Bufetov A. I., Shirai T., Proceedings of the Japan Academy Series A: Mathematical Sciences 2017 Vol. 93 No. 1 P. 1-5
In this note, we show that determinantal point processes on the real line corresponding to de Branges spaces of entire functions are rigid in the sense of Ghosh-Peres and, under certain additional assumptions, quasi-invariant under the group of diffeomorphisms of the line with compact support. ...
Added: March 14, 2017
Silvanovich O. V., Shirokov N. A., Vestnik St. Petersburg University: Mathematics 2018 Vol. 51 No. 3 P. 267-275
For more than a century, the constructive description of functional classes in terms of the possible rate of approximation of its functions by means of functions chosen from a certain set remains among the most important problems of approximation theory. It turns out that the nonuniformity of the approximation rate due between the points of ...
Added: November 26, 2018
Baranov A., Belov Y., Borichev А., Studia Mathematica 2017 Vol. 236 P. 127-142
We describe the radial Fock type spaces which have Riesz bases of normalized reproducing kernels and which are (or are not) isomorphic to de Branges spaces in terms of weight functions. ...
Added: June 7, 2017