Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pluricomplex Green Functions on Stein Manifolds and Certain Linear
  Topological Invariants   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 Fr\'echet 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 the existence of
pluricomplex Green functions and the diametral dimension of O(M). This led us
to consider negative plurisubharmonic functions on M with a nontrivial
relatively compact sublevel set (semi-proper). In section 2, we characterize
Stein manifolds possessing a semi-proper negative plurisubharmonic function
through a local version of the linear topological invariant Omega-Tilda, of
D.Vogt. In section 3 we look into pluri-Greenian complex manifolds introduced
by E.Poletsky. We show that a complex manifold is locally uniformly
pluri-Greenian if and only if it is pluri-Greenian and give a characterization
of locally uniformly uniformly pluri-Greenian Stein manifolds in terms of
notions introduced in section 2.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph