Proceedings of the Japan Academy, Series A, Mathematical Sciences

Hartogs-Osgood theorem for separately harmonic functions

Sachiko Hamano

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Abstract

Let $h$ be a separately harmonic function on an open neighborhood of a $(m-1)$-dimensional compact submanifold $\Sigma$ in R$^m$ with $m\geq 2$. We show that $h$ can be extended to a separately harmonic function on the bounded component of R$^m-\Sigma$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 83, Number 2 (2007), 16-18.

Dates
First available in Project Euclid: 5 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1173108461

Digital Object Identifier
doi:10.3792/pjaa.83.16

Mathematical Reviews number (MathSciNet)
MR2303624

Zentralblatt MATH identifier
1129.31002

Subjects
Primary: 31C05: Harmonic, subharmonic, superharmonic functions 33E99: None of the above, but in this section

Keywords
Separately harmonic potential theory

Citation

Hamano, Sachiko. Hartogs-Osgood theorem for separately harmonic functions. Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 2, 16--18. doi:10.3792/pjaa.83.16. https://projecteuclid.org/euclid.pja/1173108461


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References

  • D. H. Armitage and S. J. Gardiner, Conditions for separately subharmonic functions to be subharmonic, Potential Anal. 2 (1993), no. 3, 255–261.
  • V. Avanissian, Sur l'harmonicité des fonctions séparément harmoniques, in Séminaire de Probabilités (Univ. Strasbourg, Strasbourg, 1966/67), Vol. I, 3–17, Springer, Berlin, 1967.
  • J.-M. Hécart, Ouverts d'harmonicité pour les fonctions séparément harmoniques, Potential Anal. 13 (2000), no. 2, 115–126.
  • M. Hervé, Analytic and plurisubharmonic functions in finite and infinite dimensional spaces, Lecture Notes in Math., 198, Springer, Berlin, 1971.
  • S. Kołodziej and J. Thorbiörnson, Separately harmonic and subharmonic functions, Potential Anal. 5 (1996), no. 5, 463–466.
  • P. Lelong, Fonctions plurisousharmoniques et fonctions analytiques de variables réelles, Ann. Inst. Fourier (Grenoble) 11 (1961), 515–562.
  • J. Siciak, Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of $C^{n}$, Ann. Polon. Math. 22 (1969/1970), 145–171.
  • J. Siciak, Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of C$^n$, Ann. Polon. Math. 22 (1969), 145-171.
  • E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, 32, Princeton University Press, 1971.
  • J. Wiegerinck, Separately subharmonic functions need not be subharmonic, Proc. Amer. Math. Soc. 104 (1988), no. 3, 770–771.
  • U. Cegrell and H. Yamaguchi, Representation of magnetic fields by jump theorem for harmonic functions. (to appear).
  • V. P. Zaharjuta, Separately analytic functions, generalizations of the Hartogs theorem, and envelopes of holomorphy, Mat. Sb. (N.S.) 101(143) (1976), no. 1, 57–76, 159.