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Izv. Akad. Nauk SSSR Ser. Mat., 1967, Volume 31, Issue 1, Pages 149–160 (Mi izv2533)  

This article is cited in 1 scientific paper (total in 1 paper)

Harmonic functions representable by integrals of Green type. I

E. D. Solomentsev


Abstract: We introduce the concepts of an integral of Green–Lebesgue type and the integral of Green–Lebesgue which generalizes the classical representation of a harmonic function inside a closed surface $S$ by means of Green's formula. We give conditions for representability of a harmonic function by integrals of the above types. In this part of the work we consider the case of the unit sphere $S$.

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English version:
Mathematics of the USSR-Izvestiya, 1967, 1:1, 139–149

Bibliographic databases:

UDC: 517.5
MSC: 26A42
Received: 13.06.1966

Citation: E. D. Solomentsev, “Harmonic functions representable by integrals of Green type. I”, Izv. Akad. Nauk SSSR Ser. Mat., 31:1 (1967), 149–160; Math. USSR-Izv., 1:1 (1967), 139–149

Citation in format AMSBIB
\Bibitem{Sol67}
\by E.~D.~Solomentsev
\paper Harmonic functions representable by integrals of Green type.~I
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1967
\vol 31
\issue 1
\pages 149--160
\mathnet{http://mi.mathnet.ru/izv2533}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=224853}
\zmath{https://zbmath.org/?q=an:0162.16502|0164.41902}
\transl
\jour Math. USSR-Izv.
\yr 1967
\vol 1
\issue 1
\pages 139--149
\crossref{https://doi.org/10.1070/IM1967v001n01ABEH000551}


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  • http://mi.mathnet.ru/eng/izv/v31/i1/p149

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    This publication is cited in the following articles:
    1. E. D. Solomentsev, “Harmonic functions representable by Green's integrals. II”, Math. USSR-Izv., 1:4 (1967), 807–826  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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