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Matematicheskie Zametki, 2022, Volume 112, Issue 5, Pages 705–717
DOI: https://doi.org/10.4213/mzm13778 (Mi mzm13778) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Eta-Invariants for Parameter-Dependent Operators Associated with an Action of a Discrete Group

K. N. Zhuikov, A. Yu. Savin

Peoples' Friendship University of Russia, Moscow
Full-text PDF (553 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm13778
Abstract: $\eta$-invariants for a class of parameter-dependent nonlocal operators associated with an isometric action of a discrete group of polynomial growth on a smooth closed manifold are studied. The $\eta$-invariant is defined as the regularization of the winding number. The formula for the variation of the $\eta$-invariant when the operator changes is obtained. The results are based on the study of asymptotic expansions of traces of parameter-dependent nonlocal operators.
Keywords: elliptic operator, parameter-dependent operator, nonlocal operator, $\eta$-invariant.
Funding agency Grant number
Russian Foundation for Basic Research 21-51-12006
The work was supported in part by Young Russian Mathematics award as well as by RFBR and DFG, project number 21-51-12006.
Received: 02.06.2022
English version:
Mathematical Notes, 2022, Volume 112, Issue 5, Pages 685–696
DOI: https://doi.org/10.1134/S0001434622110062
Bibliographic databases:
Document Type: Article
UDC: 515.168.5
Language: Russian
Citation: K. N. Zhuikov, A. Yu. Savin, “Eta-Invariants for Parameter-Dependent Operators Associated with an Action of a Discrete Group”, Mat. Zametki, 112:5 (2022), 705–717; Math. Notes, 112:5 (2022), 685–696
Citation in format AMSBIB
\Bibitem{ZhuSav22}
\by K.~N.~Zhuikov, A.~Yu.~Savin
\paper Eta-Invariants for Parameter-Dependent Operators Associated with an Action of a Discrete Group
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 5
\pages 705--717
\mathnet{http://mi.mathnet.ru/mzm13778}
\crossref{https://doi.org/10.4213/mzm13778}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538800}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 5
\pages 685--696
\crossref{https://doi.org/10.1134/S0001434622110062}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85145409886}
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    • This publication is cited in the following 1 articles:
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