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Contemporary Mathematics. Fundamental Directions, 2023, Volume 69, Issue 4, Pages 599–620
DOI: https://doi.org/10.22363/2413-3639-2023-69-4-599-620
(Mi cmfd517)
 

This article is cited in 1 scientific paper (total in 1 paper)

Eta-invariant of elliptic parameter-dependent boundary-value problems

K. N. Zhuikov, A. Yu. Savin

RUDN University, Moscow, Russia
Full-text PDF (366 kB) Citations (1)
References:
Abstract: In this paper, we study the eta-invariant of elliptic parameter-dependent boundary value problems and its main properties. Using Melrose's approach, we define the eta-invariant as a regularization of the winding number of the family. In this case, the regularization of the trace requires obtaining the asymptotics of the trace of compositions of invertible parameter-dependent boundary value problems for large values of the parameter. Obtaining the asymptotics uses the apparatus of pseudodifferential boundary value problems and is based on the reduction of parameter-dependent boundary value problems to boundary value problems with no parameter.
Keywords: eta-invariant, elliptic parameter-dependent boundary value problem, pseudodifferential boundary value problem, Boutet de Monvel operator, regularized trace.
Funding agency Grant number
Contest «Young Russian Mathematics»
Russian Foundation for Basic Research 21-51-12006
This work was supported in part by the Young Russian Mathematics award and by RFBR and DFG, project No. 21-51-12006.
Bibliographic databases:
Document Type: Article
UDC: 517.954
Language: Russian
Citation: K. N. Zhuikov, A. Yu. Savin, “Eta-invariant of elliptic parameter-dependent boundary-value problems”, CMFD, 69, no. 4, PFUR, M., 2023, 599–620
Citation in format AMSBIB
\Bibitem{ZhuSav23}
\by K.~N.~Zhuikov, A.~Yu.~Savin
\paper Eta-invariant of elliptic parameter-dependent boundary-value problems
\serial CMFD
\yr 2023
\vol 69
\issue 4
\pages 599--620
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd517}
\crossref{https://doi.org/10.22363/2413-3639-2023-69-4-599-620}
\edn{https://elibrary.ru/YQAARE}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Современная математика. Фундаментальные направления
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