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 CMFD, 2019, Volume 65, Issue 4, Pages 672–682 (Mi cmfd395)

On the algebra of operators corresponding to the union of smooth submanifolds

D. A. Poluektova, A. Yu. Savin, B. Yu. Sternin

Peoples' Friendship University of Russia (RUDN University), Moscow, Russia

Abstract: For a pair of smooth transversally intersecting submanifolds in some enveloping smooth manifold, we study the algebra generated by pseudodifferential operators and (co)boundary operators corresponding to submanifolds. We establish that such an algebra has 18 types of generating elements. For operators from this algebra, we define the concept of symbol and obtain the composition formula.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-31-00176_ìîë_à16-01-00373_à19-01-00574

DOI: https://doi.org/10.22363/2413-3639-2019-65-4-672-682

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UDC: 917.986.3

Citation: D. A. Poluektova, A. Yu. Savin, B. Yu. Sternin, “On the algebra of operators corresponding to the union of smooth submanifolds”, Proceedings of the S.M. Nikolskii Mathematical Institute of RUDN University, CMFD, 65, no. 4, RUDN University, M., 2019, 672–682

Citation in format AMSBIB
\Bibitem{PolSavSte19} \by D.~A.~Poluektova, A.~Yu.~Savin, B.~Yu.~Sternin \paper On the algebra of operators corresponding to the union of smooth submanifolds \inbook Proceedings of the S.M. Nikolskii Mathematical Institute of RUDN University \serial CMFD \yr 2019 \vol 65 \issue 4 \pages 672--682 \publ RUDN University \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd395} \crossref{https://doi.org/10.22363/2413-3639-2019-65-4-672-682}