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Mathematics of the USSR-Sbornik, 1972, Volume 18, Issue 1, Pages 45–59
DOI: https://doi.org/10.1070/SM1972v018n01ABEH001610
(Mi sm3216)
 

This article is cited in 11 scientific papers (total in 11 papers)

Pseudodifferential operators on a class of noncompact manifolds

V. S. Rabinovich
References:
Abstract: This paper introduces a new class of pseudodifferential (p.d.) operators acting in spaces of Bessel potentials of section-distributions over a noncompact (in the usual sense) manifold $M$ compactified by a set of points at infinity. Two-sided $L_p$ bounds are given for the factor-norm of a p.d. operator in the subspace of compact operators using the norm of its symbol. Necessary and sufficient conditions are given for the operators to be Noetherian, and well-posed problems are investigated on manifolds of the above structure with noncompact boundary.
Bibliography: 18 titles.
Received: 15.06.1971
Bibliographic databases:
UDC: 517.43+517.948
MSC: 58G15
Language: English
Original paper language: Russian
Citation: V. S. Rabinovich, “Pseudodifferential operators on a class of noncompact manifolds”, Math. USSR-Sb., 18:1 (1972), 45–59
Citation in format AMSBIB
\Bibitem{Rab72}
\by V.~S.~Rabinovich
\paper Pseudodifferential operators on a~class of noncompact manifolds
\jour Math. USSR-Sb.
\yr 1972
\vol 18
\issue 1
\pages 45--59
\mathnet{http://mi.mathnet.ru/eng/sm3216}
\crossref{https://doi.org/10.1070/SM1972v018n01ABEH001610}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=324486}
\zmath{https://zbmath.org/?q=an:0243.58005}
Linking options:
  • https://www.mathnet.ru/eng/sm3216
  • https://doi.org/10.1070/SM1972v018n01ABEH001610
  • https://www.mathnet.ru/eng/sm/v131/i1/p46
  • This publication is cited in the following 11 articles:
    1. V. S. Rabinovich, “Method of Potential Operators for Interaction Problems on Unbounded Hypersurfaces in $\mathbb{R}^{n}$ for Dirac Operators”, Russ. J. Math. Phys., 30:4 (2023), 674  crossref
    2. Vladimir S. Rabinovich, “FREDHOLM PROPERTY OF INTERACTION PROBLEMS ON UNBOUNDED $C^{2}-$ HYPERSURFACES IN $\mathbb{R}^{n}$ FOR DIRAC OPERATORS”, J Math Sci, 271:2 (2023), 136  crossref
    3. Vladimir Rabinovich, “Fredholm property and essential spectrum of 3-D Dirac operators with regular and singular potentials”, Complex Variables and Elliptic Equations, 67:4 (2022), 938  crossref
    4. V. Rabinovich, “Two-Dimensional Dirac Operators with Interactions on Unbounded Smooth Curves”, Russ. J. Math. Phys., 28:4 (2021), 524  crossref
    5. Vladimir Rabinovich, “Lp -theory of boundary integral operators for domains with unbounded smooth boundary”, Georgian Mathematical Journal, 23:4 (2016), 595  crossref
    6. Frank-Olme Speck, Operator Theory, Pseudo-Differential Equations, and Mathematical Physics, 2013, 391  crossref
    7. R. Duduchava, F.-O. Speck, “Pseudodifferential Operators on Compact Manifolds with Lipschitz Boundary”, Math Nachr, 160:1 (2009), 149  crossref  mathscinet
    8. Luís P. Castro, Roland Duduchava, Frank-Olme Speck, Factorization, Singular Operators and Related Problems, 2003, 73  crossref
    9. Elmar Schrohe, “Fréchet Algebra Techniques for Boundary Value Problems on Noncompact Manifolds: Fredholm Criteria and Functional Calculus via Spectral Invariance”, Math Nachr, 199:1 (1999), 145  crossref  mathscinet  zmath
    10. F.-O. Speck, R. Duduchava, “Bessel potential operators for the quarter-plane”, Applicable Analysis, 45:1-4 (1992), 49  crossref  mathscinet  zmath
    11. Erhard Meister, Lecture Notes in Mathematics, 827, Ordinary and Partial Differential Equations, 1980, 182  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:327
    Russian version PDF:131
    English version PDF:24
    References:65
     
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