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On the symbol of nonlocal operators in Sobolev spaces

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Abstract

We consider nonlocal operators generated by pseudodifferential operators and the operator of shift along the trajectories of an arbitrary diffeomorphism of a smooth closed manifold. We introduce the notion of symbol of such operators acting in Sobolev spaces. As examples, we consider specific diffeomorphisms, namely, isometries and dilations.

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References

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia, Moscow, Russia

    A. Yu. Savin

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  1. A. Yu. Savin
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Original Russian Text © A.Yu. Savin, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 6, pp. 890–893.

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Savin, A.Y. On the symbol of nonlocal operators in Sobolev spaces. Diff Equat 47, 897–900 (2011). https://doi.org/10.1134/S0012266111060176

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  • DOI: https://doi.org/10.1134/S0012266111060176

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