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 Mat. Sb., 2011, Volume 202, Number 10, Pages 99–130 (Mi msb7737)

On the index of elliptic operators for the group of dilations

A. Yu. Savinab, B. Yu. Sterninba

a Leibniz University of Hannover
b Peoples Friendship University of Russia

Abstract: We investigate nonlocal operators associated with the operators of compression and expansion. We obtain an ellipticity condition, which implies that the problem has the Fredholm property, compute the index, and study how the index depends on the exponent of the Sobolev space in which the problem is considered.
Bibliography: 15 titles.

Keywords: operators of compression and expansion, nonlocal theory, ellipticity, finiteness theorem, index.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7737

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English version:
Sbornik: Mathematics, 2011, 202:10, 1505–1536

Bibliographic databases:

UDC: 515.168.5+517.956.22
MSC: Primary 58J20; Secondary 47A20, 35S05

Citation: A. Yu. Savin, B. Yu. Sternin, “On the index of elliptic operators for the group of dilations”, Mat. Sb., 202:10 (2011), 99–130; Sb. Math., 202:10 (2011), 1505–1536

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb7737
• https://doi.org/10.4213/sm7737
• http://mi.mathnet.ru/eng/msb/v202/i10/p99

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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, “On the Index of Nonlocal Elliptic Operators Corresponding to a Nonisometric Diffeomorphism”, Math. Notes, 90:5 (2011), 701–714
2. A. Savin, B. Sternin, “Index of elliptic operators for diffeomorphisms of manifolds”, J. Noncommut. 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
5. N. R. Izvarina, “On the symbol of nonlocal operators associated with a parabolic diffeomorphism”, Eurasian Math. J., 9:2 (2018), 34–43
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