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Mat. Sb. (N.S.), 1979, Volume 110(152), Number 2(10), Pages 189–217 (Mi msb2440)  

This article is cited in 27 scientific papers (total in 27 papers)

Surface integrals in a Banach space

A. V. Uglanov


Abstract: Surface integrals in a Banach space are defined and their properties are investigated. The results obtained are used for solving some problems in the theory of generalized functions and differential equations on an infinite-dimensional space.
Bibliography: 6 titles.

Full text: PDF file (2599 kB)
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English version:
Mathematics of the USSR-Sbornik, 1981, 38:2, 175–199

Bibliographic databases:

UDC: 513.88:517.948
MSC: Primary 28A75, 58C35; Secondary 28A15, 46F25, 47A70, 35A08, 35D05, 35R15
Received: 06.12.1977

Citation: A. V. Uglanov, “Surface integrals in a Banach space”, Mat. Sb. (N.S.), 110(152):2(10) (1979), 189–217; Math. USSR-Sb., 38:2 (1981), 175–199

Citation in format AMSBIB
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\by A.~V.~Uglanov
\paper Surface integrals in a~Banach space
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 110(152)
\issue 2(10)
\pages 189--217
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\transl
\jour Math. USSR-Sb.
\yr 1981
\vol 38
\issue 2
\pages 175--199
\crossref{https://doi.org/10.1070/SM1981v038n02ABEH001227}
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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. Belyaev A., “An Integral-Representation of Functions Harmonic in a Domain of Hilbert-Space”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1981, no. 6, 44–47  mathscinet  zmath  isi
    2. A. A. Belyaev, “Solution of the Dirichlet problem in a subspace of a Hilbert space using potentials”, Russian Math. Surveys, 37:4 (1982), 99–100  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. E. I. Efimova, A. V. Uglanov, “Green's formula on a Hilbert space”, Math. USSR-Sb., 47:1 (1984), 215–222  mathnet  crossref  mathscinet  zmath
    4. Uglanov A., “The Division of Generalized-Functions of Infinite Number of Derivatives by Polynomials”, 264, no. 5, 1982, 1096–1099  mathscinet  zmath  isi
    5. Belyaev A., “The Mean-Value Theorem for Harmonic-Functions in the Hilbert-Space”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1982, no. 5, 32–35  mathscinet  zmath  isi
    6. Efimova E. Uglanov A., “Formulas of the Vector Analysis in Banach-Space”, 271, no. 6, 1983, 1302–1306  mathscinet  isi
    7. Uglanov A., “Integral-Representation of Functions in Banach-Space”, 282, no. 4, 1985, 800–804  mathscinet  zmath  isi
    8. N. V. Norin, “An extended stochastic integral for non-Gaussian measures in locally convex spaces”, Russian Math. Surveys, 41:3 (1986), 229–230  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. Smolianov O., “Derham Currents and Stokes-Formula in Hilbert-Space”, 286, no. 3, 1986, 554–558  mathscinet  isi
    10. A. V. Uglanov, “The Newton–Leibniz formula on Banach spaces and approximation of functions of an infinite-dimensional argument”, Math. USSR-Izv., 30:1 (1988), 145–161  mathnet  crossref  mathscinet  zmath
    11. Piunihin S., “Finite Co-Degree Differential Forms and Stokes-Formula in Locally Convex-Spaces”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1989, no. 5, 22–26  mathscinet  isi
    12. 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
    13. A. V. Uglanov, “The Fubini's theorem for vector-valued measures”, Math. USSR-Sb., 69:2 (1991), 453–463  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. Dyachkin O., “Some Parabolic and Elliptic-Equations on Hilbert-Space”, Differ. Equ., 26:4 (1990), 468–477  mathnet  mathscinet  zmath  isi
    15. Bogachev V., “Distributions for Analytical Functionals of Random-Processes”, 312, no. 6, 1990, 1291–1296  mathscinet  zmath  isi
    16. V. I. Bogachev, “Functionals of random processes and infinite-dimensional oscillatory integrals connected with them”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 235–266  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. M. O. Smolyanova, “Stochastic approximation of Banach-valued random variables with smooth distributions”, Math. Notes, 58:3 (1995), 970–982  mathnet  crossref  mathscinet  zmath  isi
    18. Uglanov A., “Surface Integrals in Linear Topological Spaces”, Dokl. Akad. Nauk, 344:4 (1995), 450–453  mathnet  mathscinet  zmath  isi
    19. A. V. Uglanov, “Surface integrals in Frechet spaces”, Sb. Math., 189:11 (1998), 1719–1737  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. O. V. Pugachev, “Surface measures in infinite-dimensional spaces”, Math. Notes, 63:1 (1998), 94–101  mathnet  crossref  crossref  mathscinet  zmath  isi
    21. O. V. Pugachev, “The Gauss-Ostrogradskii formula in infinite-dimensional space”, Sb. Math., 189:5 (1998), 757–770  mathnet  crossref  crossref  mathscinet  zmath  isi
    22. O. V. Pugachev, “Construction of non-Gaussian surface measures by the Malliavin method”, Math. Notes, 65:3 (1999), 315–325  mathnet  crossref  crossref  mathscinet  zmath  isi
    23. É. Yu. Shamarova, “Approximation of Surface Measures in a Locally Convex Space”, Math. Notes, 72:4 (2002), 551–568  mathnet  crossref  crossref  mathscinet  zmath  isi
    24. NADEZDA A. SIDOROVA, “THE SMOLYANOV SURFACE MEASURE ON TRAJECTORIES IN A Riemannian MANIFOLD”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top, 07:03 (2004), 461  crossref  mathscinet
    25. ILYA V. TELYATNIKOV, “SMOLYANOV–WEIZSÄCKER SURFACE MEASURES GENERATED BY DIFFUSIONS ON THE SET OF TRAJECTORIES IN Riemannian MANIFOLDS”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top, 11:01 (2008), 21  crossref  mathscinet  zmath
    26. E. Yu. Shamarova, N. N. Shamarov, “Differential forms on locally convex spaces and the Stokes formula”, Russian Math. (Iz. VUZ), 60:8 (2016), 74–85  mathnet  crossref  isi
    27. Bogachev V.I. Malofeev I.I., “Surface Measures Generated by Differentiable Measures”, Potential Anal., 44:4 (2016), 767–792  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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