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Eurasian Mathematical Journal, 2021, Volume 12, Number 3, Pages 57–77
DOI: https://doi.org/10.32523/2077-9879-2021-12-3-57-77
(Mi emj415)
 

This article is cited in 2 scientific papers (total in 2 papers)

$\eta$-Invariant and index for operators on the real line periodic at infinity

A. Yu. Savinab, K. N. Zhuikova

a S. M. Nikol'skii Mathematical Institute, Peoples' Friendship University of Russia (RUDN University), 6 Miklukho Maklaya St, 117198 Moscow, Russian Federation
b Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
Full-text PDF (463 kB) Citations (2)
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Abstract: We define $\eta$-invariants for periodic pseudodifferential operators on the real line and establish their main properties. In particular, it is proved that the $\eta$-invariant satisfies logarithmic property and a formula for the derivative of the $\eta$-invariant of an operator family with respect to the parameter is obtained. Furthermore, we establish an index formula for elliptic pseudodifferential operators on the real line periodic at infinity. The contribution of infinity to the index formula is given by the constructed $\eta$-invariant. Finally, we compute $\eta$-invariants of differential operators in terms of the spectrum of their monodromy matrices.
Keywords and phrases: elliptic operator, operator with periodic coefficients, $\eta$-invariant, index.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-03-2020-223/3 (FSSF-2020-0018)
This work is supported by the Ministry of Science and Higher Education of the Russian Federation: agreement no. 075-03-2020-223/3 (FSSF-2020-0018).
Received: 31.07.2021
Bibliographic databases:
Document Type: Article
MSC: 58J20, 58J28, 58J40
Language: English
Citation: A. Yu. Savin, K. N. Zhuikov, “$\eta$-Invariant and index for operators on the real line periodic at infinity”, Eurasian Math. J., 12:3 (2021), 57–77
Citation in format AMSBIB
\Bibitem{SavZhu21}
\by A.~Yu.~Savin, K.~N.~Zhuikov
\paper $\eta$-Invariant and index for operators on the real line periodic at infinity
\jour Eurasian Math. J.
\yr 2021
\vol 12
\issue 3
\pages 57--77
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\crossref{https://doi.org/10.32523/2077-9879-2021-12-3-57-77}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85123897955}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Eurasian Mathematical Journal
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