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

This article is cited in 2 scientific papers (total in 2 papers)

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

Full text: PDF file (542 kB)
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English version:
Sbornik: Mathematics, 2016, 207:4, 519–536

Bibliographic databases:

Document Type: Article
UDC: 517.518.88
MSC: 47A53
Received: 20.05.2015

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  mathnet  crossref  isi
    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  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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