ONE-DIMENSIONAL FINITE-GAP SCHRÖDINGER OPERATORS AS A LIMIT OF COMMUTING DIFFERENCE OPERATORS

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In this paper we show that the one–dimensional finite–gap Schrödinger operator can be obtained by passing to the limit from a second–order difference operator that commutes with some odd–order difference operator; the coefficients of these difference operators are functions defined on the line and depend on a small parameter. Moreover, the spectral curve of the difference operators does not depend on the small parameter and coincides with the spectral curve of the Schrödinger operator.

Sobre autores

G. Mauleshova

Novosibirsk State University; Sobolev Institute of Mathematics

Autor responsável pela correspondência
Email: mauleshova@math.nsc.ru
Russian Federation, Novosibirsk; Russian Federation, Novosibirsk

A. Mironov

Novosibirsk State University; Sobolev Institute of Mathematics

Autor responsável pela correspondência
Email: mironov@math.nsc.ru
Russian Federation, Novosibirsk; Russian Federation, Novosibirsk

Bibliografia

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Declaração de direitos autorais © Г.С. Маулешова, А.Е. Миронов, 2023