Abstract
We give a characterization of Stein manifolds M for which the space of analytic functions,O(M), is isomorphic as Fréchet spaces to the space of analytic functions on a polydisc interms of the existence of a plurisubharmonic function on M with certain properties. We discuss some corollaries of this result and give some examples.
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I would like to thank the referee for drawing my attention to [24], which simplified the proofs of Theorem 2, and Lemma 9.
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Aytuna, A. On stein manifolds M for whichO(M) is isomorphic toO(Δn) as Fréchet spaces. Manuscripta Math 62, 297–315 (1988). https://doi.org/10.1007/BF01246835
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DOI: https://doi.org/10.1007/BF01246835