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.
\Bibitem{SavSte11}
\by A.~Yu.~Savin, B.~Yu.~Sternin
\paper On the index of elliptic operators for the group of dilations
\jour Sb. Math.
\yr 2011
\vol 202
\issue 10
\pages 1505--1536
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Linking options:
https://www.mathnet.ru/eng/sm7737
https://doi.org/10.1070/SM2011v202n10ABEH004197
https://www.mathnet.ru/eng/sm/v202/i10/p99
This publication is cited in the following 8 articles:
A. V. Boltachev, “On Ellipticity of Operators with Shear Mappings”, J Math Sci, 2024
A. V. Boltachev, “Ob elliptichnosti operatorov so skruchivaniyami”, SMFN, 69, no. 4, Rossiiskii universitet druzhby narodov, M., 2023, 565–577
N. R. Izvarina, “On the symbol of nonlocal operators associated with a parabolic diffeomorphism”, Eurasian Math. J., 9:2 (2018), 34–43
A. L. Skubachevskii, “Boundary-value problems for elliptic functional-differential equations and their applications”, Russian Math. Surveys, 71:5 (2016), 801–906
A. Savin, B. Sternin, “Index of elliptic operators for diffeomorphisms of manifolds”, J. Noncommut. Geom., 8:3 (2014), 695–734
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
Anton Savin, Boris Sternin, Pseudo-Differential Operators, Generalized Functions and Asymptotics, 2013, 1
A. Yu. Savin, “On the Index of Nonlocal Elliptic Operators Corresponding to a Nonisometric Diffeomorphism”, Math. Notes, 90:5 (2011), 701–714
Citation in format AMSBIB
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