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Some Resolvent Estimates in Harmonic Analysis

Dahlner, Anders LU (2003)
Abstract (Swedish)
Popular Abstract in Swedish

I avhandlingen studeras olika resolvent uppskattningar i harmonisk analys.



I det första arbetet visas en Wiener taubersats med hjälp av resolventtransformen.



I det andra arbetet studeras kvantitativa förfiningar av Wieners lemma i kommutativa kvasi-Banachalgebror och även i Banachalgebror.



Det tredje arbetet behandlar den klassiska Cesàro-operatorn och dess verkan på det viktade Bergmanrummet.
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... (More)
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 quasi-Banach) 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. (Less)
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author
supervisor
opponent
  • Siskakis, Aristomenis
organization
publishing date
type
Thesis
publication status
published
subject
keywords
field theory, Number Theory, algebra, algebraic geometry, Talteori, group theory, Tauberian theorem. Quantitative inversion. Cesaro operator. Bishops property beta., algebraisk geometri, fältteori, gruppteori
pages
86 pages
publisher
Centre for Mathematical Sciences, Lund University
defense location
Matematikcentrum, Sal C, Lund.
defense date
2003-06-05 13:15
external identifiers
  • other:ISRN:LUNFMA-1020-2003
ISSN
1404-0034
ISBN
91-628-5726-6
language
English
LU publication?
yes
id
065fdfc5-7eb7-41cc-ac95-1b098067386d (old id 465925)
date added to LUP
2007-09-27 15:03:42
date last changed
2018-05-29 10:17:45
@phdthesis{065fdfc5-7eb7-41cc-ac95-1b098067386d,
  abstract     = {This thesis contains three papers about three different estimates of resolvents in harmonic analysis. These papers are:<br/><br>
<br/><br>
Paper 1. ``A Wiener tauberian theorem for weighted convolution algebras of zonal functions on the automorphism group of the unit disc''<br/><br>
<br/><br>
Paper 2. ``Uniform spectral radius and compact Gelfand transform''<br/><br>
<br/><br>
Paper 3. ``Decomposable extension of the Cesáro operator on the weighted Bergman space and Bishop's property (b )''<br/><br>
<br/><br>
The first paper concerns the classical resolvent transform for a commutative convolution algebra and its applications to tauberian theorems.<br/><br>
<br/><br>
The second paper concerns uniform estimates of resolvents and of inverses in commutative Banach (and quasi-Banach) algebras, in particular when the Gelfand transform is compact.<br/><br>
<br/><br>
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.},
  author       = {Dahlner, Anders},
  isbn         = {91-628-5726-6},
  issn         = {1404-0034},
  keyword      = {field theory,Number Theory,algebra,algebraic geometry,Talteori,group theory,Tauberian theorem. Quantitative inversion. Cesaro operator. Bishops property beta.,algebraisk geometri,fältteori,gruppteori},
  language     = {eng},
  pages        = {86},
  publisher    = {Centre for Mathematical Sciences, Lund University},
  school       = {Lund University},
  title        = {Some Resolvent Estimates in Harmonic Analysis},
  year         = {2003},
}