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A Wiener Tauberian Theorem for weighted convolution algebras of zonal functions on the automorphism group of the unit disc

Dahlner, Anders LU (2006) Conference on Bergman Spaces and Related Topics in Complex Analysis 404. p.67-102
Abstract
Our main result gives necessary and sufficient conditions, in terms of Fourier transforms, for an ideal in the algebra L-1(G parallel to K, omega), the convolution algebra of zonal functions on the automorphism group on the unit disc which are integrable with respect to the weight; function omega, to be dense in the algebra, or to have as closure an ideal of functions whose set of common zeros of the Fourier transforms is a finite set on the boundary of the maximal ideal space of the algebra. The weights considered behave like Legendre functions of the first kind.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
transform, resolvent, Wiener Tauberian Theorem, estimates of Legendre functions
host publication
Bergman Spaces and Related Topics in Complex Analysis, Proceedings
volume
404
pages
67 - 102
publisher
American Mathematical Society (AMS)
conference name
Conference on Bergman Spaces and Related Topics in Complex Analysis
conference location
Barcelona, Spain
conference dates
2003-11-20 - 2003-11-22
external identifiers
  • wos:000238476900005
ISSN
0271-4132
1098-3627
language
English
LU publication?
yes
id
6c005204-30ff-4b0f-885a-94a98a7e655e (old id 1410648)
date added to LUP
2016-04-01 12:00:23
date last changed
2018-11-21 20:02:44
@inproceedings{6c005204-30ff-4b0f-885a-94a98a7e655e,
  abstract     = {Our main result gives necessary and sufficient conditions, in terms of Fourier transforms, for an ideal in the algebra L-1(G parallel to K, omega), the convolution algebra of zonal functions on the automorphism group on the unit disc which are integrable with respect to the weight; function omega, to be dense in the algebra, or to have as closure an ideal of functions whose set of common zeros of the Fourier transforms is a finite set on the boundary of the maximal ideal space of the algebra. The weights considered behave like Legendre functions of the first kind.},
  author       = {Dahlner, Anders},
  booktitle    = {Bergman Spaces and Related Topics in Complex Analysis, Proceedings},
  issn         = {0271-4132},
  language     = {eng},
  pages        = {67--102},
  publisher    = {American Mathematical Society (AMS)},
  title        = {A Wiener Tauberian Theorem for weighted convolution algebras of zonal functions on the automorphism group of the unit disc},
  volume       = {404},
  year         = {2006},
}