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An extremal function for the multiplier algebra of the universal Pick space

Wikström, Frank LU (2004) In Illinois Journal of Mathematics 48(3). p.1053-1065
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.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
Illinois Journal of Mathematics
volume
48
issue
3
pages
1053 - 1065
publisher
University of Illinois
external identifiers
  • scopus:17044409182
ISSN
0019-2082
language
English
LU publication?
no
id
021f6850-8ccf-4d7b-adad-74b253462232 (old id 1314621)
alternative location
http://www.math.uiuc.edu/~hildebr/ijm/fall04/final/wikstrom.pdf
date added to LUP
2009-05-19 13:30:08
date last changed
2017-01-13 13:34:41
@article{021f6850-8ccf-4d7b-adad-74b253462232,
  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.},
  author       = {Wikström, Frank},
  issn         = {0019-2082},
  language     = {eng},
  number       = {3},
  pages        = {1053--1065},
  publisher    = {University of Illinois},
  series       = {Illinois Journal of Mathematics},
  title        = {An extremal function for the multiplier algebra of the universal Pick space},
  volume       = {48},
  year         = {2004},
}