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 Mat. Sb., 1994, Volume 185, Number 3, Pages 117–159 (Mi msb888)

Transfer of an extension of the algebra of pseudodifferential operators, and some nonlocal elliptic problems

B. Yu. Sternin, V. E. Shatalov

M. V. Lomonosov Moscow State University

Abstract: Finiteness theorems (the Fredholm property) are proved in this paper for a certain class of elliptic problems. The operators corresponding to these problems are obtained as the elements of an extension of the set of pseudodifferential operators via a special class of (nonlocal) operators.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 81:2, 363–396

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J40, 58G20, 35S15; Secondary 47G30, 47A60, 58G15

Citation: B. Yu. Sternin, V. E. Shatalov, “Transfer of an extension of the algebra of pseudodifferential operators, and some nonlocal elliptic problems”, Mat. Sb., 185:3 (1994), 117–159; Russian Acad. Sci. Sb. Math., 81:2 (1995), 363–396

Citation in format AMSBIB
\Bibitem{SteSha94} \by B.~Yu.~Sternin, V.~E.~Shatalov \paper Transfer of an extension of the~algebra of pseudodifferential operators, and some nonlocal elliptic problems \jour Mat. Sb. \yr 1994 \vol 185 \issue 3 \pages 117--159 \mathnet{http://mi.mathnet.ru/msb888} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1268800} \zmath{https://zbmath.org/?q=an:0840.35132} \transl \jour Russian Acad. Sci. Sb. Math. \yr 1995 \vol 81 \issue 2 \pages 363--396 \crossref{https://doi.org/10.1070/SM1995v081n02ABEH003543} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RB51300006} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. B. Yu. Sternin, V. E. Shatalov, “Relative elliptic theory and the Sobolev problem”, Sb. Math., 187:11 (1996), 1691–1720
2. Korovina M., “On Zeta-Function of Operators Associated with the Smooth Manifolds”, Dokl. Akad. Nauk, 368:1 (1999), 10–13
3. Korovina M., “Investigation of the Zeta-Function of Operators Corresponding to a Class of Nonlocal Elliptic Problems”, Differ. Equ., 35:8 (1999), 1077–1086
4. Korovina M., “On Self-Adjoint Extension of Schrodinger Operator with Potential Concentrated of the Smooth Manifold”, Dokl. Akad. Nauk, 366:6 (1999), 738–740
5. Korovina M., “The Construction of a Self-Adjoint Extension of the Schro-Dinger Operator with Potential Concentrated on a Pencil of Planes: I”, Differ. Equ., 38:6 (2002), 816–829
6. Korovina M., “Construction of a Self-Adjoint Extension of the Schrodinger Operator with a Potential Concentrated on a Pencil of Planes: II”, Differ. Equ., 39:1 (2003), 73–82
7. Korovina M., “Elliptic Problems on Stratified Manifolds in Spaces with Asymptotics: II”, Differ. Equ., 40:6 (2004), 827–838
8. Korovina M., “Elliptic Problems on Stratified Manifolds in Spaces with Asymptotics: I”, Differ. Equ., 40:2 (2004), 227–240
9. A. L. Skubachevskii, “Nonclassical boundary value problems. I”, Journal of Mathematical Sciences, 155:2 (2008), 199–334
10. Korovina, MV, “Relative elliptic operators and the Sobolev problem: II”, Differential Equations, 43:4 (2007), 525
11. Korovina M.V., “Relative Elliptic Operators and the Sobolev Problem: I”, Differ. Equ., 43:3 (2007), 381–395
12. Korovina M.V., “The Algebra of Relative Morphisms on Stratified Manifolds”, Dokl. Math., 75:1 (2007), 108–111
13. Korovina, MV, “Relative elliptic morphisms and some of their applications”, Doklady Mathematics, 77:2 (2008), 226
14. Korovina M.V., “Sobolev Problem on a Stratified Manifold”, Differ. Equ., 44:1 (2008), 115–123
15. A. L. Skubachevskii, “Nonclassical boundary-value problems. II”, Journal of Mathematical Sciences, 166:4 (2010), 377–561
16. Boris Yu. Sternin, “On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem”, centr.eur.j.math, 2011
17. A. Yu. Savin, B. Yu. Sternin, “On the index of nonlocal elliptic operators associated with fibrations”, Dokl. Math, 89:1 (2014), 61
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