Uniformization of nonlocal elliptic operators and KK-theory
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By a pseudodifferential uniformization of a nonlocal elliptic operator we mean the procedure of reducing the operator to a pseudodifferential operator with a controlled modification of the index. In the paper, we suggest an approach to solving the uniformization problem; this approach uses the reduction of the symbol of a nonlocal operator to the symbol of a pseudodifferential operator. The technical apparatus here is Kasparov’s KK-theory.
KeywordsCompact Operator Elliptic Operator Short Exact Sequence Cotangent Bundle Fredholm Property
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- 2.A. B. Antonevich and A. V. Lebedev, “Functional Equations and Functional Operator Equations. A C*-Algebraic Approach,” Proc. of the St. Petersburg Math. Soc. VI, 199 of Amer. Math. Soc. Transl. Ser. 2, 25–116 (Amer. Math. Soc., Providence, RI, 2000).Google Scholar
- 5.A. Savin and B. Sternin, “Elliptic Theory for Operators Associated with Diffeomorphisms of Smooth Manifolds,” Pseudo-Differential Operators, Generalized Functions and Asymptotics 231, OperatorTheory: Advances and Applications (Birkhäuser, 1–26, 2013) arXiv:1207.3017.Google Scholar
- 9.A. Savin and B. Sternin, “Index of Elliptic Operators for Diffeomorphisms of Manifolds,” J. Noncommutative Geometry 7 (2013); arXiv:1106.4195.Google Scholar
- 15.A. Antonevich, M. Belousov and A. Lebedev, Functional Differential Equations. II. C*-Applications. Parts 1, 2 (Number 94, 95 in Pitman Monographs and Surveys in Pure and Applied Mathematics. Longman, Harlow, 1998).Google Scholar