## Functiones et Approximatio Commentarii Mathematici

### Spaces of analytic functions on essentially pluripolar compacta

Vyacheslav Zakharyuta

#### Abstract

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 $\left( \Omega \right)$.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 59, Number 1 (2018), 141-152.

Dates
First available in Project Euclid: 28 March 2018

https://projecteuclid.org/euclid.facm/1522202464

Digital Object Identifier
doi:10.7169/facm/1729

Mathematical Reviews number (MathSciNet)
MR3858284

Zentralblatt MATH identifier
06979914

#### Citation

Zakharyuta, Vyacheslav. Spaces of analytic functions on essentially pluripolar compacta. Funct. Approx. Comment. Math. 59 (2018), no. 1, 141--152. doi:10.7169/facm/1729. https://projecteuclid.org/euclid.facm/1522202464

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