Geodesic
Application of the method of similar operators to some classes of difference operators
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 14-27

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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.
Keywords: method of similar operators, eigenvalue, spectral projector, bi-invariant subspace. 
@article{INTO_2023_225_a1,
     author = {A. G. Baskakov and G. V. Garkavenko and N. B. Uskova},
     title = {Application of the method of similar operators to some classes of difference operators},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {14--27},
     publisher = {mathdoc},
     volume = {225},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_225_a1/}
}
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A. G. Baskakov; G. V. Garkavenko; N. B. Uskova. Application of the method of similar operators to some classes of difference operators. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 14-27. http://geodesic.mathdoc.fr/item/INTO_2023_225_a1/