Geodesic
On the index of elliptic operators for the group of dilations
Sbornik. Mathematics, Tome 202 (2011) no. 10, pp. 1505-1536

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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. 
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     title = {On the index of elliptic operators for the group of dilations},
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A. Yu. Savin; B. Yu. Sternin. On the index of elliptic operators for the group of dilations. Sbornik. Mathematics, Tome 202 (2011) no. 10, pp. 1505-1536. http://geodesic.mathdoc.fr/item/SM_2011_202_10_a4/