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Homogenization of the Levy-type operators. / Жижина, Елена Анатольевна; Пятницкий, Андрей Львович; Слоущ, Владимир Анатольевич; Суслина, Татьяна Александровна.

In: Functional Analysis and its Applications, Vol. 59, No. 3, 01.09.2025, p. 251-257.

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

Harvard

Жижина, ЕА, Пятницкий, АЛ, Слоущ, ВА & Суслина, ТА 2025, 'Homogenization of the Levy-type operators', Functional Analysis and its Applications, vol. 59, no. 3, pp. 251-257. https://doi.org/10.1134/S1234567825030036

APA

Жижина, Е. А., Пятницкий, А. Л., Слоущ, В. А., & Суслина, Т. А. (2025). Homogenization of the Levy-type operators. Functional Analysis and its Applications, 59(3), 251-257. https://doi.org/10.1134/S1234567825030036

Vancouver

Жижина ЕА, Пятницкий АЛ, Слоущ ВА, Суслина ТА. Homogenization of the Levy-type operators. Functional Analysis and its Applications. 2025 Sep 1;59(3):251-257. https://doi.org/10.1134/S1234567825030036

Author

Жижина, Елена Анатольевна ; Пятницкий, Андрей Львович ; Слоущ, Владимир Анатольевич ; Суслина, Татьяна Александровна. / Homogenization of the Levy-type operators. In: Functional Analysis and its Applications. 2025 ; Vol. 59, No. 3. pp. 251-257.

BibTeX

@article{6629c952e1b6466093eea2f7c80c1e46,
title = "Homogenization of the Levy-type operators",
abstract = "Abstract: In, we consider a selfadjoint operator,, of the form (Formula presented.) where. It is assumed that a function is bounded, positive definite, periodic in each variable, and is such that. A rigorous definition of the operator is given in terms of the corresponding quadratic form. It is proved that the resolvent converges in the operator norm on to the operator as. Here, is an effective operator of the same form with the constant coefficient equal to the mean value of. We obtain an error estimate of order for, for, and for. In the case where, the result is refined by taking the correctors into account.",
keywords = "Lvy-type operators, homogenization, operator error estimates",
author = "Жижина, {Елена Анатольевна} and Пятницкий, {Андрей Львович} and Слоущ, {Владимир Анатольевич} and Суслина, {Татьяна Александровна}",
year = "2025",
month = sep,
day = "1",
doi = "10.1134/S1234567825030036",
language = "English",
volume = "59",
pages = "251--257",
journal = "Functional Analysis and its Applications",
issn = "0016-2663",
publisher = "Springer Nature",
number = "3",

}

RIS

TY - JOUR

T1 - Homogenization of the Levy-type operators

AU - Жижина, Елена Анатольевна

AU - Пятницкий, Андрей Львович

AU - Слоущ, Владимир Анатольевич

AU - Суслина, Татьяна Александровна

PY - 2025/9/1

Y1 - 2025/9/1

N2 - Abstract: In, we consider a selfadjoint operator,, of the form (Formula presented.) where. It is assumed that a function is bounded, positive definite, periodic in each variable, and is such that. A rigorous definition of the operator is given in terms of the corresponding quadratic form. It is proved that the resolvent converges in the operator norm on to the operator as. Here, is an effective operator of the same form with the constant coefficient equal to the mean value of. We obtain an error estimate of order for, for, and for. In the case where, the result is refined by taking the correctors into account.

AB - Abstract: In, we consider a selfadjoint operator,, of the form (Formula presented.) where. It is assumed that a function is bounded, positive definite, periodic in each variable, and is such that. A rigorous definition of the operator is given in terms of the corresponding quadratic form. It is proved that the resolvent converges in the operator norm on to the operator as. Here, is an effective operator of the same form with the constant coefficient equal to the mean value of. We obtain an error estimate of order for, for, and for. In the case where, the result is refined by taking the correctors into account.

KW - Lvy-type operators

KW - homogenization

KW - operator error estimates

UR - https://www.mendeley.com/catalogue/79d72051-71a0-3b50-b08e-213f0872b659/

U2 - 10.1134/S1234567825030036

DO - 10.1134/S1234567825030036

M3 - Article

VL - 59

SP - 251

EP - 257

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 3

ER -

ID: 142599142