Abstract
This thesis contains three papers about three different estimates of resolvents in harmonic analysis. These papers are:
Paper 1. ``A Wiener tauberian theorem for weighted convolution algebras of zonal functions on the automorphism group of the unit disc''
Paper 2. ``Uniform spectral radius and compact Gelfand transform''
Paper 3. ``Decomposable extension of the Cesáro operator on the weighted Bergman space and Bishop's property (b )''
The first paper concerns the classical resolvent transform for a commutative convolution algebra and its applications to tauberian theorems.
The second paper concerns uniform estimates of resolvents and of inverses in commutative Banach (and quasiBanach) algebras, in particular when the Gelfand transform is compact.
In the last paper we consider the Cesáro operator and its action on weighted Bergman spaces. Using classical analysis we calculate the spectrum, produce estimates the resolvent and of its left inverse. The results are then used to retrieve operator theoretic information of the Cesáro operator on the weighted Bergman space.
Paper 1. ``A Wiener tauberian theorem for weighted convolution algebras of zonal functions on the automorphism group of the unit disc''
Paper 2. ``Uniform spectral radius and compact Gelfand transform''
Paper 3. ``Decomposable extension of the Cesáro operator on the weighted Bergman space and Bishop's property (b )''
The first paper concerns the classical resolvent transform for a commutative convolution algebra and its applications to tauberian theorems.
The second paper concerns uniform estimates of resolvents and of inverses in commutative Banach (and quasiBanach) algebras, in particular when the Gelfand transform is compact.
In the last paper we consider the Cesáro operator and its action on weighted Bergman spaces. Using classical analysis we calculate the spectrum, produce estimates the resolvent and of its left inverse. The results are then used to retrieve operator theoretic information of the Cesáro operator on the weighted Bergman space.
Original language  English 

Qualification  Doctor 
Awarding Institution 

Supervisors/Advisors 

Award date  2003 Jun 5 
Publisher  
ISBN (Print)  9162857266 
Publication status  Published  2003 
Bibliographical note
Defence detailsDate: 20030605
Time: 13:15
Place: Matematikcentrum, Sal C, Lund.
External reviewer(s)
Name: Siskakis, Aristomenis
Title: [unknown]
Affiliation: [unknown]

Paper 1. ``A Wiener tauberian theorem for weighted convolution algebras of zonal functions on the automorphism group of the unit disc''
Paper 2. ``Uniform spectral radius and compact Gelfand transform''
Paper 3. ``Decomposable extension of the Cesáro operator on the weighted Bergman space and Bishop's property (b )''
Subject classification (UKÄ)
 Mathematics
Keywords
 field theory
 Number Theory
 algebra
 algebraic geometry
 Talteori
 group theory
 Tauberian theorem. Quantitative inversion. Cesaro operator. Bishops property beta.
 algebraisk geometri
 fältteori
 gruppteori