Open Access
September 2018 Spaces of analytic functions on essentially pluripolar compacta
Vyacheslav Zakharyuta
Funct. Approx. Comment. Math. 59(1): 141-152 (September 2018). DOI: 10.7169/facm/1729


Let $A\left( K\right) $ be the locally convex space of all analytic germs on a compact subset $K$ of a Stein manifold $\Omega $, $\dim \Omega =n$, endowed with the standard inductive topogy, let $0^{n}$ denote the origin of $\mathbb{C}^{n}$, The main result is the characterisation of the isomorphism $A\left( K\right) \simeq A\left( \left\{ 0^{n}\right\} \right) $ in terms of pluripotential theory. It is based on the general result of Aytuna-Krone-Terzio\u{g}lu on the characterisation of power series spaces of infinite type in terms of interpolational invariants $\left( DN\right) $ and $\left( \Omega \right)$.


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Vyacheslav Zakharyuta. "Spaces of analytic functions on essentially pluripolar compacta." Funct. Approx. Comment. Math. 59 (1) 141 - 152, September 2018.


Published: September 2018
First available in Project Euclid: 28 March 2018

zbMATH: 06979914
MathSciNet: MR3858284
Digital Object Identifier: 10.7169/facm/1729

Primary: 32015 , 46A63
Secondary: 32E10 , 46A04

Keywords: complete pluripolarity , interpolation invariants , spaces of analytic functions

Rights: Copyright © 2018 Adam Mickiewicz University

Vol.59 • No. 1 • September 2018
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