Functiones et Approximatio Commentarii Mathematici

Spaces of analytic functions on essentially pluripolar compacta

Vyacheslav Zakharyuta

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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

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

First available in Project Euclid: 28 March 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

complete pluripolarity spaces of analytic functions interpolation invariants


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.

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