Functiones et Approximatio Commentarii Mathematici

Spaces of analytic functions on essentially pluripolar compacta

Vyacheslav Zakharyuta

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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

Permanent link to this document
https://projecteuclid.org/euclid.facm/1522202464

Digital Object Identifier
doi:10.7169/facm/1729

Mathematical Reviews number (MathSciNet)
MR3858284

Zentralblatt MATH identifier
06979914

Subjects
Primary: 32015 46A63: Topological invariants ((DN), ($\Omega$), etc.)
Secondary: 46A04: Locally convex Fréchet spaces and (DF)-spaces 32E10: Stein spaces, Stein manifolds

Keywords
complete pluripolarity spaces of analytic functions interpolation invariants

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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