Research Papers

Estimates of Green matrix entries of selfadjoint unbounded block Jacobi matrices

S. N. Naboko^a, S. Simonov<sup>bc

a</sup> 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

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.

Received: 11.06.2021

Language: English

 English version: St. Petersburg Mathematical Journal, 2024, 35:1, 185–199