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

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

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
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
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
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