Sammanfattning
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.
Originalspråk | engelska |
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Sidor (från-till) | 1053-1065 |
Tidskrift | Illinois Journal of Mathematics |
Volym | 48 |
Nummer | 3 |
Status | Published - 2004 |
Externt publicerad | Ja |
Ämnesklassifikation (UKÄ)
- Matematik
- Matematisk analys