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

Mauleshova, G. S.; Mironov, A. E.

doi:10.31857/S2686954323600349

PII

10.31857/S2686954323600349-1

DOI

10.31857/S2686954323600349

Publication type

Status

Published

Authors

G. S. Mauleshova

Affiliation:
Novosibirsk State University
Sobolev Institute of Mathematics

A. E. Mironov

Affiliation:
Novosibirsk State University
Sobolev Institute of Mathematics

Volume/ Edition

Volume 512 / Issue number 1

Pages

81-84

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.

Keywords

коммутирующие разностные операторы одномерный оператор Шрёдингера коммутирующие дифференциальные операторы

Date of publication

01.05.2023

Year of publication

2023

Number of purchasers

Views

References

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.
6. Кричевер И.М., Новиков С.П. // УМН. 2003. Т. 58. В. 3 (351). С. 51–88.
7. Маулешова Г.С., Миронов А.Е. // Тр. МИАН. 2020. Т. 310. С. 217–229.

GOST	Mauleshova G., Mironov A. ONE-DIMENSIONAL FINITE-GAP SCHRÖDINGER OPERATORS AS A LIMIT OF COMMUTING DIFFERENCE OPERATORS // Doklady Mathematics. – 2023. – V. 512. – Issue number 1 C. 81-84 . URL: https://danmathras.ru/10-31857-s2686954323600349-1/?version_id=110226. DOI: 10.31857/S2686954323600349
MLA	Mauleshova, G. S, Mironov, A. E "ONE-DIMENSIONAL FINITE-GAP SCHRÖDINGER OPERATORS AS A LIMIT OF COMMUTING DIFFERENCE OPERATORS." Doklady Mathematics. 512.1 (2023).:81-84. DOI: 10.31857/S2686954323600349
APA	Mauleshova G., Mironov A. (2023). ONE-DIMENSIONAL FINITE-GAP SCHRÖDINGER OPERATORS AS A LIMIT OF COMMUTING DIFFERENCE OPERATORS. Doklady Mathematics. vol. 512, no. 1, pp.81-84 DOI: 10.31857/S2686954323600349

RAS PresidiumДоклады Российской академии наук. Математика, информатика, процессы управления Doklady Mathematics

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

You can

References

Индексирование

RAS PresidiumДоклады Российской академии наук. Математика, информатика, процессы управления Doklady Mathematics

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

You can

References

Индексирование

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