An extension of Hartogs’ theorem for domains whose boundary is not smooth
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- by David G. Schaeffer
- Proc. Amer. Math. Soc. 25 (1970), 714-715
- DOI: https://doi.org/10.1090/S0002-9939-1970-0261030-7
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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.References
- 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, vol. 3, Tata Institute of Fundamental Research, Bombay; Oxford University Press, London, 1967. MR 0212575
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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