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Transactions of the American Mathematical Society

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CR functions and tube manifolds


Author: M. Kazlow
Journal: Trans. Amer. Math. Soc. 255 (1979), 153-171
MSC: Primary 32A07; Secondary 32D05
DOI: https://doi.org/10.1090/S0002-9947-1979-0542875-5
MathSciNet review: 542875
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Abstract: Various generalizations of Bochner's theorem on the extension of holomorphic functions over tube domains are considered. It is shown that CR functions on tubes over connected, locally closed, locally starlike subsets of $ {\textbf{R}^n}$ uniquely extend to CR functions on almost all of the convex hull of the tube set. A CR extension theorem on maximally stratified real submanifolds of $ {\textbf{C}^n}$ is proven. The above two theorems are used to show that the CR functions (resp. CR distributions) on tubes over a fairly general class of submanifolds of $ {\textbf{R}^n}$ uniquely extend to CR functions (CR distributions) on almost all of the convex hull.


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DOI: https://doi.org/10.1090/S0002-9947-1979-0542875-5
Article copyright: © Copyright 1979 American Mathematical Society

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