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

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

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.

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

Full text: PDF file (781 kB)
References: PDF file   HTML file

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

Bibliographic databases:

Document Type: Article
UDC: 515.168.5+517.956.22
MSC: Primary 58J20; Secondary 47A20, 35S05
Received: 11.05.2010 and 08.02.2011

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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  • 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  mathnet  crossref  crossref  mathscinet  isi
    2. A. Savin, B. Sternin, “Index of elliptic operators for diffeomorphisms of manifolds”, J. Noncommut. Geom., 8:3 (2014), 695–734  crossref  mathscinet  zmath  isi  elib
    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  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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