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Mat. Sb. (N.S.), 1982, Volume 119(161), Number 2(10), Pages 225–232 (Mi msb2845)  

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

Green's formula on a Hilbert space

E. I. Efimova, A. V. Uglanov


Abstract: The first Green's formula for integrals on a Hilbert space is proved. Using this formula the authors establish, in particular, the following result.
Theorem. A nondegenerate quadratic functional of a Wiener random process has an infinitely differentiate distribution function.
Bibliography: 9 titles.

Full text: PDF file (421 kB)
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English version:
Mathematics of the USSR-Sbornik, 1984, 47:1, 215–222

Bibliographic databases:

UDC: 517.98
MSC: Primary 46C99, 46G12; Secondary 28A15, 28C20, 58C20
Received: 06.07.1981

Citation: E. I. Efimova, A. V. Uglanov, “Green's formula on a Hilbert space”, Mat. Sb. (N.S.), 119(161):2(10) (1982), 225–232; Math. USSR-Sb., 47:1 (1984), 215–222

Citation in format AMSBIB
\Bibitem{EfiUgl82}
\by E.~I.~Efimova, A.~V.~Uglanov
\paper Green's formula on a Hilbert space
\jour Mat. Sb. (N.S.)
\yr 1982
\vol 119(161)
\issue 2(10)
\pages 225--232
\mathnet{http://mi.mathnet.ru/msb2845}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=675194}
\zmath{https://zbmath.org/?q=an:0524.46027|0506.46030}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 47
\issue 1
\pages 215--222
\crossref{https://doi.org/10.1070/SM1984v047n01ABEH002638}


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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. Efimova E., Uglanov A., “Formulas of the Vector Analysis in Banach-Space”, 271, no. 6, 1983, 1302–1306  mathscinet  isi
    2. Smolianov O., “Derham Currents and Stokes-Formula in Hilbert-Space”, 286, no. 3, 1986, 554–558  mathscinet  isi
    3. V. I. Bogachev, O. G. Smolyanov, “Analytic properties of infinite-dimensional distributions”, Russian Math. Surveys, 45:3 (1990), 1–104  mathnet  crossref  mathscinet  zmath  isi
    4. Dyachkin O., “Some Parabolic and Elliptic-Equations on Hilbert-Space”, Differ. Equ., 26:4 (1990), 468–477  mathnet  mathscinet  zmath  isi
    5. A. I. Kirillov, “Infinite-dimensional analysis and quantum theory as semimartingale calculus”, Russian Math. Surveys, 49:3 (1994), 43–95  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. V. I. Bogachev, “Differentiable measures and the Malliavin calculus”, Journal of Mathematical Sciences (New York), 87:4 (1997), 3577  crossref  mathscinet  zmath
    7. O. V. Pugachev, “The Gauss-Ostrogradskii formula in infinite-dimensional space”, Sb. Math., 189:5 (1998), 757–770  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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