Affiliation:
1. Novosibirsk State University
2. Sobolev Institute of Mathematics
Abstract
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.
Publisher
The Russian Academy of Sciences
Reference7 articles.
1. Маулешова Г.С., Миронов А.Е. // ДАН. 2018. Т. 478. В. 4. С. 392–394.
2. Новиков С.П. // Функц. анализ и его прил. 1974. Т. 8. В. 3. С. 54–66.
3. Итс А.Р., Матвеев В.Б. //ТМФ. 1975. Т. 23. В. 1. С. 51–68.
4. Кричевер И.М. // УМН. 1978. Т. 33. В. 4 (202). С. 215–216.
5. Mumford D. // Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977). Kinokuniya. Tokyo. 1978. 115–153.