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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Finite order vanishing of boundary values of holomorphic mappings


Author: Mitja Lakner
Journal: Proc. Amer. Math. Soc. 112 (1991), 521-527
MSC: Primary 30E25
MathSciNet review: 1065952
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Abstract: Suppose that $ f$ is a holomorphic function on a half-disc in the complex plane that extends continuously to the diameter $ E$, such that the extension maps $ E$ to a double cone with the vertex at the origin. If the extension $ f{\vert _E}$ has an isolated zero at the origin, then $ f$ vanishes to finite order at 0.


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

  • [1] S. Alinhac, M. S. Baouendi, and L. P. Rothchild, Unique continuation and regularity for holomorphic functions at the boundary, preprint, 1989.
  • [2] S. Bell and L. Lempert, A $ {C^\infty }$ Schwarz reflection principle in one and several complex variables, preprint, 1989.
  • [3] W. Rudin, Real and complex analysis, McGraw-Hill, New York, 1970.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1065952-2
PII: S 0002-9939(1991)1065952-2
Keywords: Holomorphic function, order of zero, index
Article copyright: © Copyright 1991 American Mathematical Society