Domains of Holomorphy

Junjiro Noguchi ()
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Junjiro Noguchi: The University of Tokyo

Chapter Chapter 5 in Analytic Function Theory of Several Variables, 2016, pp 155-201 from Springer

Abstract: Abstract A domain of holomorphy is defined as a domain with no boundary point b such that there is a neighborhood V of b and all holomorphic functions on the domain analytically extend over V (no Hartogs’ phenomenon happens at any boundary point). We first discuss the logarithmic convexity of Reinhardt domains, where every holomorphic function is expanded to a convergent power series. We prove that a domain is holomorphically convex if and only if it is a domain of holomorphy (Cartan–Thullen).

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-0291-5_5

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DOI: 10.1007/978-981-10-0291-5_5

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