Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 52, No. 1, pp. 61-94 (1995)

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On the Indicator of Growth of Entire Functions of Exponential Type in Infinite Dimensional Spaces and the Levi Problem in Infinite Dimensional Projective Spaces

Masaru Nishihara

Department of Mathematics, Fukuoka Institute of Technology,
Wajiro, Fukuoka 811-02 - JAPAN

Abstract: Let $E$ be a separable complex Fréchet space with the bounded approximation property, or a complex DFN-space and $\bfc{P}(E)$ be the complex projective space induced from $E$. Then we solve affirmatively the Levi problem in a Riemann domain over the projective space $\bfc{P}(E)$. By using this result, we give the infinite dimensional version of the indicator theorem of entire functions of exponential type on $\bfc{C}^{n}$.

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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.

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