Abstract:In this paper we explore the existence of pluricomplex Green functions for Stein manifolds from a functional analysis point of view. For a Stein manifold M , we will denote by O (M ) the Fréchet space of analytic functions on M equipped with the topology of uniform convergence on compact subsets. In the first section, we examine the relationship between existence of pluricomplex Green functions and the diametral dimension of O (M ) .This led us to consider negative plurisubharmonic functions on M with a nontri… Show more
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