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An extremal function for the multiplier algebra of the universal Pick space
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
2004 (English)In: Illinois Journal of Mathematics, ISSN 0019-2082, Vol. 48, no 3, 1053-1065 p.Article in journal (Refereed) Published
Abstract [en]

Let $H^2_m$ be the Hilbert function space on the unit ball in $C{m}$ defined by the kernel $k(z,w) = (1-langle z,w rangle)^{-1}$. For any weak zero set of the multiplier algebra of $H^2_m$, we study a natural extremal function, $E$. We investigate the properties of $E$ and show for example that $E$ tends to $0$ at almost every boundary point. We also give several explicit examples of the extremal function and compare the behaviour of $E$ to the behaviour of $delta^*$ and $g$, the corresponding extremal function for $H^infty$ and the pluricomplex Green function, respectively.

Place, publisher, year, edition, pages
2004. Vol. 48, no 3, 1053-1065 p.
Keyword [en]
Pick interpolation, extremal functions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-3809Local ID: 4548OAI: oai:DiVA.org:miun-3809DiVA: diva2:28841
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2011-01-10Bibliographically approved

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CiteExportLink to record
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  • apa
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