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 Mat. Sb., 2016, Volume 207, Number 4, Pages 47–64 (Mi msb8543)

Geometric and operator measures of degeneracy for the set of solutions to the Stieltjes matrix moment problem

Yu. M. Dyukarev

V. N. Karazin Kharkiv National University, Ukraine

Abstract: The ranks of the limit Weyl intervals are known to serve as the geometric measure of degeneracy of the solution set to a Stieltjes matrix moment problem. This paper puts forward the first operator measure of degeneracy for the solution set to a Stieltjes matrix moment problem in terms of the deficiency vectors of a pair of associated positive symmetric operators. A relationship between the geometric and operator measures of degeneracy for a Stieltjes matrix moment problem is established, from which some corollaries about the Stieltjes matrix moment problem are obtained.
Bibliography 19 titles.

Keywords: the Stieltjes matrix moment problem, Weyl intervals, Weyl discs, symmetric operators, deficiency vectors.

DOI: https://doi.org/10.4213/sm8543

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English version:
Sbornik: Mathematics, 2016, 207:4, 519–536

Bibliographic databases:

Document Type: Article
UDC: 517.518.88
MSC: 47A53

Citation: Yu. M. Dyukarev, “Geometric and operator measures of degeneracy for the set of solutions to the Stieltjes matrix moment problem”, Mat. Sb., 207:4 (2016), 47–64; Sb. Math., 207:4 (2016), 519–536

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb8543
• https://doi.org/10.4213/sm8543
• http://mi.mathnet.ru/eng/msb/v207/i4/p47

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. E. Choke Rivero, L. E. Garza Gaona, “Matrix orthogonal polynomials associated with perturbations of block Toeplitz matrices”, Russian Math. (Iz. VUZ), 61:12 (2017), 57–69
2. Yu. M. Dyukarev, “The zeros of determinants of matrix-valued polynomials that are orthonormal on a semi-infinite or finite interval”, Sb. Math., 209:12 (2018), 1745–1755
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