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Wolff's ideal problem in the multiplier algebra on dirichlet space

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dc.contributorKwon, Hyun-Kyoung
dc.contributorMidkiff, K. Clark
dc.contributorMoen, Kabe
dc.contributorMoore, Robert L.
dc.contributor.advisorTrent, Tavan T.
dc.contributor.authorBanjade, Debendra Prasad
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2017-03-01T17:08:40Z
dc.date.available2017-03-01T17:08:40Z
dc.date.issued2014
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractIn an effort to classify ideal membership for finitely-generated ideals in H<super>&infin</super> (D), Wolff [G] proved that: If {f <sub>j</sub>}<sub>j=1</sub><super> j=n</super>&subset H<super>&infin</super> (D), H &belongs H<super>&infin</super> (D) and |H(z)| &le (&sum |f<sub>j</sub>}<sub>(z)|<super> 2</super>)<super>&half</super> for all z in D then H <super> 3</super>&belongs I ({f<sub>j</sub>}), the ideal generated by {f<sub>j</sub>} in H<super>&infin</super> (D). In the first part of this dissertation, we establish an analogue of Wolff's result for the algebra of multipliers on Dirichlet space. In the second part, we extend this result to the multiplier algebra on weighted Dirichlet space with the weight &alpha in (0,1). Finally, we will prove a general ideal problem. We provide the best known sufficient condition for when H itself is in the ideal.en_US
dc.format.extent83 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0001575
dc.identifier.otherBanjade_alatus_0004D_12023
dc.identifier.urihttps://ir.ua.edu/handle/123456789/2031
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.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectMathematics
dc.titleWolff's ideal problem in the multiplier algebra on dirichlet spaceen_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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