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.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:
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
- 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
- 2023-04-20 15:25:53
@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}}, keywords = {{transform; resolvent; Wiener Tauberian Theorem; estimates of Legendre functions}}, 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}}, }