Geodesic
On bounded difference operators with involution
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 12-21

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In this paper, we considers difference operators of a special type (with involution) whose infinite matrix has two nonzero diagonals. We introduce the notion of an abstract involution operator and examine its such as invertibility, spectrum, and commutability condition. Also, we discuss the problem of whether the original operator and its inverse belong to special operator classes.
Keywords: difference operator, involution, abstract involution, spectrum, invertibility, commutability 
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     author = {A. G. Baskakov and G. V. Garkavenko and N. B. Uskova},
     title = {On bounded difference operators with involution},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {12--21},
     publisher = {mathdoc},
     volume = {229},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_229_a1/}
}
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A. G. Baskakov; G. V. Garkavenko; N. B. Uskova. On bounded difference operators with involution. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 12-21. http://geodesic.mathdoc.fr/item/INTO_2023_229_a1/