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Algebra i Analiz, 2023, Volume 35, Issue 1, Pages 243–261 (Mi aa1853)  
Research Papers

Estimates of Green matrix entries of selfadjoint unbounded block Jacobi matrices

S. N. Nabokoa, S. Simonovbc

a Department of Mathematical Physics, Institute of Physics, St.-Petersburg State University, 198904 Ulianovskaia 1, St. Petergoff, St. Petersburg, Russia
b St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 191023 Fontanka 27, St. Petersburg, Russia
c St.-Petersburg State University, Universitetskaya nab. 7-9, 199034 St. Petersburg, Russia
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Abstract: In a wide class of block Jacobi matrices, an estimate of norms of Green matrix (resolvent) entries is proved, which depends on the rate of growth of norms of the off-diagonal entries of the matrix and on the distance from the spectral parameter to the essential spectrum if the latter is nonempty. The sharpness of this estimate is shown by an example.
Keywords: Jacobi matrix, generalized eigenvectors, orthogonal polynomials, Levinson theorem, asymptotics.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00657A
Russian Science Foundation 20-11-20032
Knut and Alice Wallenbergs Foundation
The first author was supported by the RFBR 19-01-00657A grant as well as by the Knut and Alice Wallenberg Foundation (§§1–2) and by the RScF 20-11-20032 grant (§§3–4). The second author was supported by the RFBR 19-01-00565A grant (§§1–2) and by the RScF 20-11-20032 grant (§§3–4).
Received: 11.06.2021
English version:
St. Petersburg Mathematical Journal, 2024, Volume 35, Issue 1, Pages 185–199
DOI: https://doi.org/10.1090/spmj/1800
Document Type: Article
Language: English
Citation: S. N. Naboko, S. Simonov, “Estimates of Green matrix entries of selfadjoint unbounded block Jacobi matrices”, Algebra i Analiz, 35:1 (2023), 243–261; St. Petersburg Math. J., 35:1 (2024), 185–199
Citation in format AMSBIB
\Bibitem{NabSim23}
\by S.~N.~Naboko, S.~Simonov
\paper Estimates of Green matrix entries of selfadjoint unbounded block Jacobi matrices
\jour Algebra i Analiz
\yr 2023
\vol 35
\issue 1
\pages 243--261
\mathnet{http://mi.mathnet.ru/aa1853}
\transl
\jour St. Petersburg Math. J.
\yr 2024
\vol 35
\issue 1
\pages 185--199
\crossref{https://doi.org/10.1090/spmj/1800}
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