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Fall 2004 An extremal function for the multiplier algebra of the universal Pick space
Frank Wikström
Illinois J. Math. 48(3): 1053-1065 (Fall 2004). DOI: 10.1215/ijm/1258131070

Abstract

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.

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Frank Wikström. "An extremal function for the multiplier algebra of the universal Pick space." Illinois J. Math. 48 (3) 1053 - 1065, Fall 2004. https://doi.org/10.1215/ijm/1258131070

Information

Published: Fall 2004
First available in Project Euclid: 13 November 2009

zbMATH: 1071.32026
MathSciNet: MR2114269
Digital Object Identifier: 10.1215/ijm/1258131070

Subjects:
Primary: 32U35
Secondary: 32F45, 46E22, ‎46J15, 47B32

Rights: Copyright © 2004 University of Illinois at Urbana-Champaign

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Vol.48 • No. 3 • Fall 2004
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