The Corona Theorem for the multiplier algebras on weighted Dirichlet spaces

dc.contributorWang, James L.
dc.contributorLiem, Vo T.
dc.contributorBorie, Richard B.
dc.contributorWu, Zhijian
dc.contributor.advisorTrent, Tavan T.
dc.contributor.authorKidane, Berhanu Tekle
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2017-02-28T22:22:08Z
dc.date.available2017-02-28T22:22:08Z
dc.date.issued2009
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractIn this dissertation we give a proof of "The Corona Theorem for Infinitely Many Functions for the Multiplier Algebras on Weighted Dirichlet Spaces", and we obtain explicit estimates on the size of the solution. We denote the open unit disc of the complex plane by D, and for α in (0, 1) we denote by Dα the Weighted Dirichlet Spaces of all holomorphic functions on D, and byen_US
dc.description.abstractfen_US
dc.description.abstractα the weighted Dirichlet norm. To prove the Dα Corona Theorem and find a bound for the solution we use a similar technique employed by Trent [Tr 2] in his proof of the corona theorem for Dirichlet space. The first challenge is to find a norm that is expressed on the boundary of D. In this dissertation we first establish such a norm. The new norm basically enables us to extend multipliers on the weighted Dirichlet spaces to multipliers on a related weighted harmonic Dirichlet spaces. Finally using Schur's Theorem and Cauchy's Transform we are able to prove the the weighted Dirichlet corona theorem and give a bound for the solution.en_US
dc.format.extent100 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0000148
dc.identifier.otherKidane_alatus_0004D_10184
dc.identifier.urihttps://ir.ua.edu/handle/123456789/654
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectMathematics
dc.titleThe Corona Theorem for the multiplier algebras on weighted Dirichlet spacesen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Mathematics
etdms.degree.disciplineMathematics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.
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