Finite order vanishing of boundary values of holomorphic mappings
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- by Mitja Lakner PDF
- Proc. Amer. Math. Soc. 112 (1991), 521-527 Request permission
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 $f{|_E}$ has an isolated zero at the origin, then $f$ vanishes to finite order at 0.References
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S. Alinhac, M. S. Baouendi, and L. P. Rothchild, Unique continuation and regularity for holomorphic functions at the boundary, preprint, 1989.
S. Bell and L. Lempert, A ${C^\infty }$ Schwarz reflection principle in one and several complex variables, preprint, 1989.
W. Rudin, Real and complex analysis, McGraw-Hill, New York, 1970.
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 521-527
- MSC: Primary 30E25
- DOI: https://doi.org/10.1090/S0002-9939-1991-1065952-2
- MathSciNet review: 1065952