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Mat. Sb. (N.S.), 1972, Volume 88(130), Number 4(8), Pages 504–521 (Mi msb3193)  

This article is cited in 10 scientific papers (total in 10 papers)

Hypoelliptic differential equations and pseudodifferential operators with operator-valued symbols

V. V. Grushin


Abstract: Sufficient conditions are established for the hypoellipticity of pseudodifferential operators with operator-valued symbols. These results are used to prove the hypoellipticity of new classes of linear partial differential equations.
Bibliography: 43 titles.

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English version:
Mathematics of the USSR-Sbornik, 1972, 17:4, 497–514

Bibliographic databases:

UDC: 517.9
MSC: Primary 35H05, 35S05; Secondary 47G05
Received: 11.06.1971

Citation: V. V. Grushin, “Hypoelliptic differential equations and pseudodifferential operators with operator-valued symbols”, Mat. Sb. (N.S.), 88(130):4(8) (1972), 504–521; Math. USSR-Sb., 17:4 (1972), 497–514

Citation in format AMSBIB
\Bibitem{Gru72}
\by V.~V.~Grushin
\paper Hypoelliptic differential equations and pseudodifferential operators with operator-valued symbols
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 88(130)
\issue 4(8)
\pages 504--521
\mathnet{http://mi.mathnet.ru/msb3193}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=316879}
\zmath{https://zbmath.org/?q=an:0243.35020}
\transl
\jour Math. USSR-Sb.
\yr 1972
\vol 17
\issue 4
\pages 497--514
\crossref{https://doi.org/10.1070/SM1972v017n04ABEH001599}


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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. A. V. Fursikov, “On a class of globally hypoelliptic operators”, Math. USSR-Sb., 20:3 (1973), 383–405  mathnet  crossref  mathscinet  zmath
    2. Yu. V. Egorov, “Subelliptic operators”, Russian Math. Surveys, 30:2 (1975), 59–118  mathnet  crossref  mathscinet  zmath
    3. S. A. Smagin, “Meromorphicity of $P^z$, where $P$ is a matrix”, Funct. Anal. Appl., 9:1 (1975), 83–84  mathnet  crossref  mathscinet  zmath
    4. S. A. Smagin, “Complex powers of hypoelliptic systems in $\mathbf R^n$”, Math. USSR-Sb., 28:3 (1976), 291–300  mathnet  crossref  mathscinet  zmath  isi
    5. V. V. Grushin, “Construction of a parametrix for degenerate elliptic operators by the method of double-scale asymptotic expansions”, Funct. Anal. Appl., 11:2 (1977), 143–144  mathnet  crossref  mathscinet  zmath
    6. A. I. Karol', “Operator-valued pseudodifferential operators and the resolvent of a degenerate elliptic operator”, Math. USSR-Sb., 49:2 (1984), 553–567  mathnet  crossref  mathscinet  zmath
    7. V. P. Maslov, “Non-standard characteristics in asymptotic problems”, Russian Math. Surveys, 38:6 (1983), 1–42  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. G. G. Kazaryan, “On a functional index of hypoellipticity”, Math. USSR-Sb., 56:2 (1987), 333–347  mathnet  crossref  mathscinet  zmath
    9. Toshihiko Hoshiro, “On Levi-type conditions for hypoellipticity of certain diffrential operators”, Communications in Partial Differential Equations, 17:5-6 (1992), 905  crossref
    10. T. Matsuzawa, “Gevery hypoellipticity of the grushin operators and the heat kernel method”, Integral Transforms and Special Functions, 6:1-4 (1998), 63  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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