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Trace formulas for Schrödinger operators on periodic graphs. / Korotyaev, Evgeny; Сабурова, Наталья.

в: Journal of Mathematical Analysis and Applications, Том 508, № 2, 125888, 15.04.2022.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Korotyaev, E & Сабурова, Н 2022, 'Trace formulas for Schrödinger operators on periodic graphs', Journal of Mathematical Analysis and Applications, Том. 508, № 2, 125888. https://doi.org/10.1016/j.jmaa.2021.125888

APA

Korotyaev, E., & Сабурова, Н. (2022). Trace formulas for Schrödinger operators on periodic graphs. Journal of Mathematical Analysis and Applications, 508(2), [125888]. https://doi.org/10.1016/j.jmaa.2021.125888

Vancouver

Korotyaev E, Сабурова Н. Trace formulas for Schrödinger operators on periodic graphs. Journal of Mathematical Analysis and Applications. 2022 Апр. 15;508(2). 125888. https://doi.org/10.1016/j.jmaa.2021.125888

Author

Korotyaev, Evgeny ; Сабурова, Наталья. / Trace formulas for Schrödinger operators on periodic graphs. в: Journal of Mathematical Analysis and Applications. 2022 ; Том 508, № 2.

BibTeX

@article{6c1239dcc8bc4e7689f3a77dab3c53fa,

title = "Trace formulas for Schr{\"o}dinger operators on periodic graphs",

abstract = "We consider Schr{\"o}dinger operators with periodic potentials on periodic discrete graphs. Their spectrum consists of a finite number of bands. We determine trace formulas for the Schr{\"o}dinger operators. The proof is based on the decomposition of the Schr{\"o}dinger operators into a direct integral and a specific representation of fiber operators. The traces of the fiber operators are expressed as finite Fourier series of the quasimomentum. The coefficients of the Fourier series are given in terms of the potentials and cycles in the quotient graph from some specific cycle sets. We also present the trace formulas for the heat kernel and the resolvent of the Schr{\"o}dinger operators and the determinant formulas.",

keywords = "Discrete Schr{\"o}dinger operators, Periodic graphs, Trace formulas",

author = "Evgeny Korotyaev and Наталья Сабурова",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2022",

month = apr,

day = "15",

doi = "10.1016/j.jmaa.2021.125888",

language = "English",

volume = "508",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Elsevier",

number = "2",

}

RIS

TY - JOUR

T1 - Trace formulas for Schrödinger operators on periodic graphs

AU - Korotyaev, Evgeny

AU - Сабурова, Наталья

PY - 2022/4/15

Y1 - 2022/4/15

N2 - We consider Schrödinger operators with periodic potentials on periodic discrete graphs. Their spectrum consists of a finite number of bands. We determine trace formulas for the Schrödinger operators. The proof is based on the decomposition of the Schrödinger operators into a direct integral and a specific representation of fiber operators. The traces of the fiber operators are expressed as finite Fourier series of the quasimomentum. The coefficients of the Fourier series are given in terms of the potentials and cycles in the quotient graph from some specific cycle sets. We also present the trace formulas for the heat kernel and the resolvent of the Schrödinger operators and the determinant formulas.

AB - We consider Schrödinger operators with periodic potentials on periodic discrete graphs. Their spectrum consists of a finite number of bands. We determine trace formulas for the Schrödinger operators. The proof is based on the decomposition of the Schrödinger operators into a direct integral and a specific representation of fiber operators. The traces of the fiber operators are expressed as finite Fourier series of the quasimomentum. The coefficients of the Fourier series are given in terms of the potentials and cycles in the quotient graph from some specific cycle sets. We also present the trace formulas for the heat kernel and the resolvent of the Schrödinger operators and the determinant formulas.

KW - Discrete Schrödinger operators

KW - Periodic graphs

KW - Trace formulas

UR - http://www.scopus.com/inward/record.url?scp=85120771567&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2021.125888

DO - 10.1016/j.jmaa.2021.125888

M3 - Article

AN - SCOPUS:85120771567

VL - 508

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

M1 - 125888

ER -

ID: 91318467