An extension of Hartogs’ theorem for domains whose boundary is not smooth
Author:
David G. Schaeffer
Journal:
Proc. Amer. Math. Soc. 25 (1970), 714-715
MSC:
Primary 32.20
DOI:
https://doi.org/10.1090/S0002-9939-1970-0261030-7
MathSciNet review:
0261030
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Abstract | References | Similar Articles | Additional Information
Abstract: In this note we obtain an extension of Hartogs’ theorem on analytic continuation inside a bounded domain in ${C^n}$ which requires no assumption on the smoothness of the boundary. The standard proof of Hartogs’ theorem applies with the minor change of using a Whitney function as the boundary data.
- Lars Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0203075
- B. Malgrange, Ideals of differentiable functions, Tata Institute of Fundamental Research Studies in Mathematics, No. 3, Tata Institute of Fundamental Research, Bombay; Oxford University Press, London, 1967. MR 0212575
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Additional Information
Keywords:
Several complex variables,
pseudo-convexity,
Hartogs’ Theorem,
Whitney functions
Article copyright:
© Copyright 1970
American Mathematical Society