Complete domains with respect to the Carathéodory distance. II
Abstract: In  we have obtained the following result: Let be a bounded domain in . Suppose there is a compact subset of such that for every there is an analytic automorphism and a point such that . Then is a domain of bounded holomorphy, in the sense that is the maximal domain on which every bounded holomorphic function on can be continued holomorphically (cf. Narasimhan [2, Proposition 7, p. 127]). Here we shall give a stronger result: Under the same assumptions, is -complete. We note that a -complete domain is a domain of bounded holomorphy, in particular, a domain of holomorphy. A domain of bounded holomorphy, however, need not be -complete.
-  Dong S. Kim, Complete domains with respect to the Carathéodory distance, Proc. Amer. Math. Soc. 49 (1975), 169–174. MR 0367297, https://doi.org/10.1090/S0002-9939-1975-0367297-3
-  Raghavan Narasimhan, Several complex variables, The University of Chicago Press, Chicago, Ill.-London, 1971. Chicago Lectures in Mathematics. MR 0342725
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Keywords: -complete, analytic automorphism, bounded homogeneous domain
Article copyright: © Copyright 1975 American Mathematical Society