Geodesic
Spectral properties of one infinite tridiagonal matrix
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 31-42

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Using the method of similar operators, we obtain conditions under which an infinite tridiagonal matrix can be transformed to the diagonal (block-diagonal) form by a similarity transformation. Asymptotic estimates of the eigenvalues and eigenvectors are also obtained.
Mots-clés : infinite tridiagonal matrices
Keywords: eigenvalue, eigenvector, method of similar operators. 
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G. V. Garkavenko; N. B. Uskova. Spectral properties of one infinite tridiagonal matrix. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 31-42. http://geodesic.mathdoc.fr/item/INTO_2021_199_a3/