One-Dimensional Finite-Gap Schrödinger Operators As a Limit of Commuting Difference Operators

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One-Dimensional Finite-Gap Schrödinger Operators As a Limit of Commuting Difference Operators. / Mauleshova, G. S.; Mironov, A. E.

In: Doklady Mathematics, Vol. 108, No. 1, 13, 08.2023, p. 312-315.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{214d4bdeafaf43b89ff85d8fe6057f4e,

title = "One-Dimensional Finite-Gap Schr{\"o}dinger Operators As a Limit of Commuting Difference Operators",

abstract = "In this paper we show that the one-dimensional finite-gap Schr{\"o}dinger operator can be obtained via passage 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 Schr{\"o}dinger operator.",

keywords = "commuting difference operators, commuting differential operators, one-dimensional Schr{\"o}dinger operator",

author = "Mauleshova, {G. S.} and Mironov, {A. E.}",

note = "This work was supported by the Russian Science Foundation, project no. 21-41-00018.",

year = "2023",

month = aug,

doi = "10.1134/S1064562423700904",

language = "English",

volume = "108",

pages = "312--315",

journal = "Doklady Mathematics",

issn = "1064-5624",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - One-Dimensional Finite-Gap Schrödinger Operators As a Limit of Commuting Difference Operators

AU - Mauleshova, G. S.

AU - Mironov, A. E.

N1 - This work was supported by the Russian Science Foundation, project no. 21-41-00018.

PY - 2023/8

Y1 - 2023/8

N2 - In this paper we show that the one-dimensional finite-gap Schrödinger operator can be obtained via passage 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.

AB - In this paper we show that the one-dimensional finite-gap Schrödinger operator can be obtained via passage 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.

KW - commuting difference operators

KW - commuting differential operators

KW - one-dimensional Schrödinger operator

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85178462000&origin=inward&txGid=0f0d20d63486519bf5a3cb6f45c9d7cb

UR - https://elibrary.ru/item.asp?id=64279423

UR - https://www.mendeley.com/catalogue/7c488900-5415-33e1-b540-38234b33b5df/

U2 - 10.1134/S1064562423700904

DO - 10.1134/S1064562423700904

M3 - Article

VL - 108

SP - 312

EP - 315

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 1

M1 - 13

ER -

ID: 59554680