Pacific Journal of Mathematics

Mean-value characterization of pluriharmonic and separately harmonic functions.

L. A. Aizenberg, C. A. Berenstein, and L. Wertheim

Article information

Source
Pacific J. Math., Volume 175, Number 2 (1996), 295-306.

Dates
First available in Project Euclid: 6 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102353146

Mathematical Reviews number (MathSciNet)
MR1432833

Zentralblatt MATH identifier
0865.31007

Subjects
Primary: 32F05
Secondary: 31B05: Harmonic, subharmonic, superharmonic functions

Citation

Aizenberg, L. A.; Berenstein, C. A.; Wertheim, L. Mean-value characterization of pluriharmonic and separately harmonic functions. Pacific J. Math. 175 (1996), no. 2, 295--306. https://projecteuclid.org/euclid.pjm/1102353146


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References

  • [1] M. Agranovsky, C.A. Berenstein, D.C. Chang and D. Pascuas, Injectivity of the Pompeiu transform in the Heisenberg group, J. Analyse Math., 63 (1994), 131-173.
  • [2] M. Agranovsky, C.A. Berenstein and D.C. Chang, Morera theorem for holornorphic Hp spaces in the Heisenberg group, J. reine angew. Math., 443 (1993), 49-89.
  • [3] L. Aizenberg, Carleman's Formulas in Complex Analysis, Kluwer Acad. Publ., Dodrecht, 1993.
  • [4] L.A. Aizenberg and Sh.A. Dautov, Differential forms orthogonal to holomorphic functions or forms, and their properties, Amer. Math. Soc, Providence, 1983.
  • [5] L.A. Aizenberg and A.P. Yuzhakov, Integral representations and residues in multidi- mensional complex analysis, Nauka, Novosibirsk, 1979. English translation, Amer. Math. Soc, Providence, 1983.
  • [6] C.A. Berenstein and R. Gay, Sur la synthese spectrale dans les espaces symmetriques, J. Math. Pures AppL, 65 (1986), 323-333.
  • [7] C.A. Berenstein and R. Gay, A localversion of the 2-circles theorem, Israel J, Math., 55 (1987), 521-544.
  • [8] C.A. Berenstein and R. Gay, Le probleme de Pompeiu local, J. Analyse Math., 52 (1989), 15-51.
  • [9] C.A. Berenstein and L. Zalcman, The Pompeiu problem in symmetric spaces, Com- ment. Math. Helvetici, 55 (1980), 593-621.
  • [10] L. Brown, B.M. Schreiber and B.A. Taylor, Spectral synthesis and the Pompeiu problem, Ann. Inst. Fourier, 23 (1973), 125-154.
  • [11] J. Delsarte, Lectures on topics in mean periodic functions and the two-radius theo- rem, Tata Institute, Bombay, 1961.
  • [12] P.A. Griffits and J. Harris, Principles of algebraic geometry, John Wiley and Sons, New York, 1978.
  • [13] L. Zalcman, Offbeat integral geometry, Amer. Math. Monthly, 87 (1980), 161-175.
  • [14] L. Zalcman, A bibliographic survey of the Pompeiu problem, Approximation by solutions of partial differential equations, B. Fuglede et al. (eds.), Kluwer Acad. Publ., (1992), 185-194.