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On the index of nonlocal elliptic operators for the group of dilations. (English. Russian original) Zbl 1213.58016
Dokl. Math. 82, No. 1, 519-522 (2010); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 433, No. 1, 21-24 (2010).
The authors consider a nonisometric case of the index problem for nonlocal elliptic operators associated with actions of discrete groups.
The isometric case was considered in the book by V. E. Nazaikinskij, A. Yu. Savin and B. Yu. Sternin [Elliptic theory and noncommutative geometry. Nonlocal elliptic operators. Operator Theory: Advances and Applications 183. Advances in Partial Differential Equations. Basel: Birkhäuser (2008; Zbl 1158.58013)].

58J05 Elliptic equations on manifolds, general theory
58J20 Index theory and related fixed-point theorems on manifolds
Full Text: DOI
[1] V. E. Nazaikinskii, A. Yu. Savin, and B. Yu. Sternin, Elliptic Theory and Noncommutative Geometry (Birkhauser, Basel, 2008). · Zbl 1158.58013
[2] A. B. Antonevich, Izv. Akad. Nauk SSSR, Ser. Mat. 53(1), 3–24 (1989).
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