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 Mat. Zametki, 2011, Volume 90, Issue 5, Pages 712–726 (Mi mz8828)

On the Index of Nonlocal Elliptic Operators Corresponding to a Nonisometric Diffeomorphism

A. Yu. Savin

Peoples Friendship University of Russia, Moscow

Abstract: We consider nonlocal elliptic operators corresponding to diffeomorphisms of smooth closed manifolds. The index of such operators is calculated. More precisely, it was shown that the index of the operator is equal to that of the elliptic boundary-value problem on the cylinder whose base is the original manifold. As an example, we study nonlocal operators on the two-dimensional Riemannian manifold corresponding to the Euler tangent operator.

Keywords: nonlocal elliptic operator, index of an elliptic operator, Riemannian manifold, elliptic boundary-value problem, diffeomorphism, Euler tangent operator, ellipticity condition, Fredholm property

DOI: https://doi.org/10.4213/mzm8828

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English version:
Mathematical Notes, 2011, 90:5, 701–714

Bibliographic databases:

UDC: 515.168.5+517.956.22
Revised: 08.02.2011

Citation: A. Yu. Savin, “On the Index of Nonlocal Elliptic Operators Corresponding to a Nonisometric Diffeomorphism”, Mat. Zametki, 90:5 (2011), 712–726; Math. Notes, 90:5 (2011), 701–714

Citation in format AMSBIB
\Bibitem{Sav11} \by A.~Yu.~Savin \paper On the Index of Nonlocal Elliptic Operators Corresponding to a Nonisometric Diffeomorphism \jour Mat. Zametki \yr 2011 \vol 90 \issue 5 \pages 712--726 \mathnet{http://mi.mathnet.ru/mz8828} \crossref{https://doi.org/10.4213/mzm8828} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2962561} \transl \jour Math. Notes \yr 2011 \vol 90 \issue 5 \pages 701--714 \crossref{https://doi.org/10.1134/S0001434611110083} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000298659000008} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-83755200054} 

• http://mi.mathnet.ru/eng/mz8828
• https://doi.org/10.4213/mzm8828
• http://mi.mathnet.ru/eng/mz/v90/i5/p712

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. Yu. Savin, B. Yu. Sternin, “On the index of elliptic operators for the group of dilations”, Sb. Math., 202:10 (2011), 1505–1536
2. Savin A., Sternin B., “Index of Elliptic Operators For Diffeomorphisms of Manifolds”, J. Noncommutative Geom., 8:3 (2014), 695–734
3. L. E. Rossovskii, “Elliptic functional differential equations with contractions and extensions of independent variables of the unknown function”, Journal of Mathematical Sciences, 223:4 (2017), 351–493
4. A. L. Skubachevskii, “Boundary-value problems for elliptic functional-differential equations and their applications”, Russian Math. Surveys, 71:5 (2016), 801–906
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