English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we explore the existence of pluricomplex Green functions forStein manifolds from a functional analysis point of view. For a Stein manifold$M$, we will denote by $O(M)$ the Fr\'echet space of analytic functions on $M$equipped with the topology of uniform convergence on compact subsets. In thefirst section, we examine the relationship between the existence ofpluricomplex Green functions and the diametral dimension of $O(M)$. This led usto consider negative plurisubharmonic functions on $M$ with a nontrivialrelatively compact sublevel set (semi-proper). In section 2, we characterizeStein manifolds possessing a semi-proper negative plurisubharmonic functionthrough a local version of the linear topological invariant $\widetilde{\Omega}$, of D.Vogt. In section 3 we look into pluri-Greenian complex manifoldsintroduced by E.Poletsky. We show that a complex manifold is locally uniformlypluri-Greenian if and only if it is pluri-Greenian and give a characterizationof locally uniformly uniformly pluri-Greenian Stein manifolds in terms ofnotions introduced in section 2.

Pluricomplex Green Functions on Stein Manifolds and Certain Linear Topological Invariants