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Mat. Sb., 2000, Volume 191, Number 5, Pages 109–142 (Mi msb479)  

This article is cited in 6 scientific papers (total in 6 papers)

On a class of pseudodifferential operators in $\mathbb R^m$ and on stratified manifolds

B. A. Plamenevskii, V. N. Senichkin

Saint-Petersburg State University

Abstract: A class of pseudodifferential operators in a subdomain of $\mathbb R^m$ that is well adapted to the transfer to manifolds with (intersecting) edges of various dimensions is considered. A version of symbolic calculus is discussed. The operators in question act in Sobolev spaces with weighted norms. Stratified manifolds (with edges as strata) are introduced and pseudodifferential operators on such manifolds are defined.

DOI: https://doi.org/10.4213/sm479

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English version:
Sbornik: Mathematics, 2000, 191:5, 725–757

Bibliographic databases:

UDC: 517.98
MSC: Primary 58G15, 47G30; Secondary 58A35
Received: 19.04.1999

Citation: B. A. Plamenevskii, V. N. Senichkin, “On a class of pseudodifferential operators in $\mathbb R^m$ and on stratified manifolds”, Mat. Sb., 191:5 (2000), 109–142; Sb. Math., 191:5 (2000), 725–757

Citation in format AMSBIB
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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. Lauter R., Pseudodifferential analysis on conformally compact spaces, Mem. Amer. Math. Soc., 163, no. 777, 2003, xvi+92 pp.  mathscinet  isi
    2. Nazaikinskii V.E., Rozenblum G., Savin A.Y., Sternin B.Y., “Guillemin transform and Toeplitz representations for operators on singular manifolds”, Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, Contemporary Mathematics Series, 366, 2005, 281–306  crossref  mathscinet  zmath  isi
    3. Nazaikinskii V.E., Savin A.Yu., Sternin B.Yu., “Pseudodifferential operators on stratified manifolds. II”, Differ. Equ., 43:5 (2007), 704–716  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Homotopy classification of elliptic operators on stratified manifolds”, Izv. Math., 71:6 (2007), 1167–1192  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Noncommutative geometry and classification of elliptic operators”, Journal of Mathematical Sciences, 164:4 (2010), 603–636  mathnet  crossref  mathscinet  elib
    6. 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
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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