Pseudoconvex Domains and Oka’s Theorem

Junjiro Noguchi ()
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Junjiro Noguchi: The University of Tokyo

Chapter Chapter 7 in Analytic Function Theory of Several Variables, 2016, pp 281-341 from Springer

Abstract: Abstract In this chapter we deal with pseudoconvex domains. In Chap. 4 we saw thatOka, Kiyoshi the Oka–Cartan Fundamental Theorem holds on holomorphically convex domains, and in Chap. 5 that a holomorphically convex domain is equivalent to a domain of holomorphy. These domains are shown to be pseudoconvex (Cartan–Thullen). The converse (Levi’s problem) was proved by K. Oka and the complete proof is presented here. We will see again that Oka’s Jôku-Ikô plays an essential role.

Date: 2016
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DOI: 10.1007/978-981-10-0291-5_7

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