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Mat. Sb. (N.S.), 1978, Volume 106(148), Number 3(7), Pages 455–483 (Mi msb2586)  

This article is cited in 6 scientific papers (total in 7 papers)

The index of random elliptic operators. II

B. V. Fedosov, M. A. Shubin


Abstract: For uniformly elliptic operators in $\mathbf R^n$ whose coefficients are smooth random functions which are homogeneous with respect to shifts in $\mathbf R^n$ the concept of an index is introduced and its properties are investigated. The index of a family of such operators is also defined. Formulas are established which express the index of an operator or a family of operators in terms of the principal symbol. Examples and special cases are considered.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Sbornik, 1979, 35:1, 131–156

Bibliographic databases:

UDC: 517.43+519.2
MSC: 47F05, 35R60
Received: 27.06.1977

Citation: B. V. Fedosov, M. A. Shubin, “The index of random elliptic operators. II”, Mat. Sb. (N.S.), 106(148):3(7) (1978), 455–483; Math. USSR-Sb., 35:1 (1979), 131–156

Citation in format AMSBIB
\Bibitem{FedShu78}
\by B.~V.~Fedosov, M.~A.~Shubin
\paper The index of random elliptic operators.~II
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 106(148)
\issue 3(7)
\pages 455--483
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=501191}
\zmath{https://zbmath.org/?q=an:0422.58025|0392.58010}
\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 1
\pages 131--156
\crossref{https://doi.org/10.1070/SM1979v035n01ABEH001459}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JB17500009}


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  • http://mi.mathnet.ru/eng/msb/v148/i3/p455

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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers

    This publication is cited in the following articles:
    1. M. A. Shubin, “The spectral theory and the index of elliptic operators with almost periodic coefficients”, Russian Math. Surveys, 34:2 (1979), 109–157  mathnet  crossref  mathscinet  zmath
    2. P. E. Dedik, M. A. Shubin, “Random pseudodifferential operators and the stabilization of solutions of parabolic equations with random coefficients”, Math. USSR-Sb., 41:1 (1982), 33–52  mathnet  crossref  mathscinet  zmath
    3. M. V. Novitskii, “On the recovery, from a countable collection of polynomial conservation laws, of action variables for the KdV equation in the class of almost periodic functions”, Math. USSR-Sb., 56:2 (1987), 417–428  mathnet  crossref  mathscinet  zmath
    4. Shubin M., “L(2) Riemann-Roch Theorem for Elliptic-Operators”, Geom. Funct. Anal., 5:2 (1995), 482–527  crossref  mathscinet  zmath  isi
    5. V. A. Sadovnichii, V. E. Podolskii, “Traces of operators”, Russian Math. Surveys, 61:5 (2006), 885–953  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Yu. A. Kordyukov, “Index theory and non-commutative geometry on foliated manifolds”, Russian Math. Surveys, 64:2 (2009), 273–391  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. M. S. Agranovich, L. A. Aizenberg, G. L. Alfimov, M. I. Vishik, T. Voronov, A. V. Karabegov, M. V. Karasev, A. A. Komech, V. P. Maslov, V. V. Pukhnachov, D. E. Tamarkin, N. N. Tarkhanov, B. L. Tsygan, M. A. Shubin, “Boris Vasil'evich Fedosov (obituary)”, Russian Math. Surveys, 67:1 (2012), 167–174  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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