Envelopes of holomorphy and extension of functions of bounded type

Details Envelopes of holomorphy and extension of functions of bounded type Envelopes of holomorphy and extension of functions of bounded type

2009-04-15

arxiv.org/abs/0904.2384v4

Advances in Mathematics 229 (2012) 2098-2121

Mathematics

Functional Analysis

25 pages

Scientific paper

10.1016/j.aim.2011.10.019

We study the extension of holomorphic functions of bounded type defined on an open subset of a Banach space, to larger domains. For this, we first characterize the envelope of holomorphy of a Riemann domain over a Banach space, with respect to the algebra of bounded type holomorphic functions, in terms of the spectrum of the algebra. We then give a simple description of the envelopes of balanced open sets and relate the concepts of domain of holomorphy and polynomial convexity. We show that for bounded balanced sets, extensions to the envelope are always of bounded type, and that this does not necessarily hold for unbounded sets, answering a question posed by Hirschowitz in 1972. We also consider extensions to open subsets of the bidual, present some Banach-Stone type results and show some properties of the spectrum when the domain is the unit ball of $\ell_p$.

Affiliated with

Also associated with

No associations

Rating

Envelopes of holomorphy and extension of functions of bounded type does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Envelopes of holomorphy and extension of functions of bounded type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Envelopes of holomorphy and extension of functions of bounded type will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-592490