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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
2016-04-01 15:36:58
date last changed
2022-01-28 06:11:10
@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}},
  url          = {{http://www.math.uiuc.edu/~hildebr/ijm/fall04/final/wikstrom.pdf}},
  volume       = {{48}},
  year         = {{2004}},
}