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A test for holomorphy in the unit ball of $ {\bf C}\sp{n}$


Author: Carlos A. Berenstein
Journal: Proc. Amer. Math. Soc. 90 (1984), 88-90
MSC: Primary 32A10
DOI: https://doi.org/10.1090/S0002-9939-1984-0722421-0
MathSciNet review: 722421
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Abstract: A new test for holomorphy in the unit ball of $ {{\mathbf{C}}^n}$ in the spirit of Morera's theorem is given.


References [Enhancements On Off] (What's this?)

  • [1] M. G. Agranovskii, Tests for holomorphy in symmetric regions, Siberian Math. J. 22 (1981), 171-179.
  • [2] C. A. Berenstein, An inverse spectral theorem and its application to the Pompeiu problem, J. Analyse Math. 37 (1980), 188-254. MR 583635 (82b:35031)
  • [3] C. A. Berenstein and M. Shahshahani, Harmonic analysis and the Pompeiu problem, Amer. J. Math. (to appear). MR 714774 (85d:32061)
  • [4] C. A. Berenstein and L. Zalcman, The Pompeiu problem in symmetric spaces, Comment. Math. Helv. 55 (1980), 593-621. MR 604716 (83d:43012)
  • [5] C. A. Berenstein and P. Yang, An overdetermined Neumann problem in the unit disk, Adv. in Math. 44 (1982), 1-17. MR 654546 (84e:35107)
  • [6] L. Brown, B. Schreiber and B. A. Taylor, Spectral synthesis and the Pompeiu problem, Ann. Inst. Fourier (Grenoble) 23 (1973), 125-154. MR 0352492 (50:4979)
  • [7] J. Globevnik, Analyticity on rotation invariant families of curves, preprint. MR 712259 (85f:30060)
  • [8] W. Rudin, Function theory in the unit ball of $ {{\mathbf{C}}^n}$, Springer-Verlag, New York, 1980. MR 601594 (82i:32002)
  • [9] S. Williams, Analyticity of the boundary of Lipschitz domains without the Pompeiu property, Indiana Univ. Math. J. 30 (1981), 357-369. MR 611225 (82j:31009)
  • [10] L. Zalcman, Analyticity and the Pompeiu problem, Arch. Rational Mech. Anal. 47 (1972), 237-254. MR 0348084 (50:582)
  • [11] -, Offbeat integral geometry, Amer. Math. Monthly 87 (1980), 161-175. MR 562919 (81b:53046)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0722421-0
Keywords: Holomorphic functions, Morera's theorem, symmetric spaces
Article copyright: © Copyright 1984 American Mathematical Society

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