Some applications of a decomposition method

Aytuna, Aydın; Terzioğlu, Tosun

doi:10.1016/s0304-0208(08)70312-8

Cited by 3 publications

(3 citation statements)

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“…For more information about the diametral dimension of spaces of analytic functions on complete Reinhardt domains in

\mathbb {C}^n

, we refer the reader to [5, 7].…”

Section: Pluricomplex Green Functions On a Stein Manifold M$m$ And Th...mentioning

confidence: 99%

Pluricomplex Green functions on Stein manifolds and certain linear topological invariants

Aytuna

2022

Bulletin of London Math Soc

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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 nontrivial relatively compact sublevel set (semi-proper). In Section 2, we characterize Stein manifolds possessing a semi-proper negative plurisubharmonic function through a local, controlled approximation type condition, which can be considered as a local version of the linear topological invariant Ω of Vogt. In Section 3, we look into pluri-Greenian and locally uniformly pluri-Greenian complex manifolds introduced by 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 pluri-Greenian Stein manifolds in terms of the notions introduced in Section 2.M S C 2 0 2 0 32A70, 32U35 (primary), 46E10 (secondary)

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“…For more information about the diametral dimension of spaces of analytic functions on complete Reinhardt domains in

\mathbb {C}^n

, we refer the reader to [5, 7].…”

Section: Pluricomplex Green Functions On a Stein Manifold M$m$ And Th...mentioning

confidence: 99%

Pluricomplex Green functions on Stein manifolds and certain linear topological invariants

Aytuna

2022

Bulletin of London Math Soc

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show abstract

“…For more information about the diametral dimension of spaces of analytic functions on complete Reinhardt domains in C n , we refer the reader to [5,7]…”

Section: Pluricomplex Green Functions On a Stein Manifold M And The D...mentioning

confidence: 99%

Pluricomplex Green Functions on Stein Manifolds and Certain Linear Topological Invariants

Aytuna¹

2021

Preprint

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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 nontrivial relatively compact sublevel set (semi-proper). In section 2, we characterize Stein manifolds possessing a semi-proper negative plurisubharmonic function through a local, controlled approximation type condition, which can be considered as a local version of the linear topological invariant Ω of D.Vogt. In Section 3 we look into pluri-Greenian and locally uniformly 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 pluri-Greenian Stein manifolds in terms of the notions introduced in Section 2.

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“…(2) H ε (A (the equivalence of the asymptotics (1) and (2) follows from the results of Mityagin [10] and Levin-Tikhomirov [9]). Kolmogorov also suggested the conjecture that in the one-dimensional case, for quite general pairs (K, D), the strong asymptotics…”

Section: Introduction the Kolmogorov Widths Of A Compact Setmentioning

confidence: 95%