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

This article is cited in 4 scientific papers (total in 4 papers)

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

Full text: PDF file (588 kB)
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English version:
Mathematical Notes, 2011, 90:5, 701–714

Bibliographic databases:

Document Type: Article
UDC: 515.168.5+517.956.22
Received: 17.05.2010
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
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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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Savin A., Sternin B., “Index of Elliptic Operators For Diffeomorphisms of Manifolds”, J. Noncommutative Geom., 8:3 (2014), 695–734  crossref  mathscinet  zmath  isi  scopus
    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  mathnet  crossref
    4. A. L. Skubachevskii, “Boundary-value problems for elliptic functional-differential equations and their applications”, Russian Math. Surveys, 71:5 (2016), 801–906  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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