An extremal function for the multiplier algebra of the universal Pick space
(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:
https://lup.lub.lu.se/record/1314621
- author
- Wikström, Frank LU
- publishing date
- 2004
- 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}},
}