| Title | An extremal function for the multiplier algebra of the universal Pick space |
| Authors | Frank Wikström |
| Alternative Location | http://www.math.uiuc.edu/~h..., Restricted Access |
| Publication | Illinois journal of mathematics |
| Year | 2004 |
| Volume | 48 |
| Issue | 3 |
| Pages | 1053 - 1065 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | University Of Illinois At Urbana-Champaign, Department of Mathematics |
| Abstract 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. |
| ISBN/ISSN/Other | ISSN: 00192082 |
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