An extremal function for the multiplier algebra of the universal Pick space
Author
Summary, in English
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.
Publishing year
2004
Language
English
Pages
1053-1065
Publication/Series
Illinois Journal of Mathematics
Volume
48
Issue
3
Links
Document type
Journal article
Publisher
University of Illinois
Topic
- Mathematics
- Mathematical Analysis
Status
Published
ISBN/ISSN/Other
- ISSN: 0019-2082