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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 1, Pages 147–178 (Mi izv1234)  

This article is cited in 3 scientific papers (total in 3 papers)

The spectrum of an algebra of pseudodifferential operators with piecewise smooth symbols

B. A. Plamenevskii, V. N. Senichkin


Abstract: The authors study the spectrum of a $C^*$-algebra of pseudodifferential operators whose symbols have discontinuities along submanifolds (the supports of the discontinuities) intersecting at nonzero angles. All (up to equivalence) irreducible representations of such algebras are enumerated, a realization of these representations is indicated, and the spectral topology is described.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:1, 147–179

Bibliographic databases:

UDC: 517.98
MSC: Primary 46L99, 58G15, 46K10; Secondary 35S05
Received: 02.03.1987

Citation: B. A. Plamenevskii, V. N. Senichkin, “The spectrum of an algebra of pseudodifferential operators with piecewise smooth symbols”, Izv. Akad. Nauk SSSR Ser. Mat., 53:1 (1989), 147–178; Math. USSR-Izv., 34:1 (1990), 147–179

Citation in format AMSBIB
\Bibitem{PlaSen89}
\by B.~A.~Plamenevskii, V.~N.~Senichkin
\paper The spectrum of an algebra of pseudodifferential operators with piecewise smooth symbols
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 1
\pages 147--178
\mathnet{http://mi.mathnet.ru/izv1234}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=992982}
\zmath{https://zbmath.org/?q=an:0713.46039|0676.46044}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 1
\pages 147--179
\crossref{https://doi.org/10.1070/IM1990v034n01ABEH000615}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. B. A. Plamenevskii, V. N. Senichkin, “Pseudodifferential Operators on Manifolds with Singularities”, Funct. Anal. Appl., 33:2 (1999), 154–156  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. B. A. Plamenevskii, V. N. Senichkin, “On a class of pseudodifferential operators in $\mathbb R^m$ and on stratified manifolds”, Sb. Math., 191:5 (2000), 725–757  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. B. A. Plamenevskii, “Solvability of the algebra of pseudodifferential operators with piecewise smooth coefficients on a smooth manifold”, St. Petersburg Math. J., 21:2 (2010), 317–351  mathnet  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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