Application of the method of similar operators to some classes of difference operators

A. G. Baskakov ; G. V. Garkavenko ; N. B. Uskova

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 14-27.

Résumé

Two second-order difference operators defined by their infinite matrices are considered: an operator with an ordinary potential and an operator with an involutive potential. The spectral properties of these operators under various conditions were performed by the method of similar operators. Results concerning the asymptotics of the eigenvalues in the case of a potential with involution are obtained.

Détail

Keywords: method of similar operators, eigenvalue, spectral projector, bi-invariant subspace.

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