A Wiener Tauberian Theorem for weighted convolution algebras of zonal functions on the automorphism group of the unit disc
(2006) Conference on Bergman Spaces and Related Topics in Complex Analysis 404. p.67102 Abstract
 Our main result gives necessary and sufficient conditions, in terms of Fourier transforms, for an ideal in the algebra L1(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:
https://lup.lub.lu.se/record/1410648
 author
 Dahlner, Anders ^{LU}
 organization
 publishing date
 2006
 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
 20031120  20031122
 external identifiers

 wos:000238476900005
 ISSN
 10983627
 02714132
 language
 English
 LU publication?
 yes
 id
 6c00520430ff4b0f885a94a98a7e655e (old id 1410648)
 date added to LUP
 20160401 12:00:23
 date last changed
 20230420 15:25:53
@inproceedings{6c00520430ff4b0f885a94a98a7e655e, abstract = {{Our main result gives necessary and sufficient conditions, in terms of Fourier transforms, for an ideal in the algebra L1(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 = {{10983627}}, keywords = {{transform; resolvent; Wiener Tauberian Theorem; estimates of Legendre functions}}, language = {{eng}}, pages = {{67102}}, 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}}, }