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

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dc.contributor Kwon, Hyun-Kyoung
dc.contributor Midkiff, K. Clark
dc.contributor Moen, Kabe
dc.contributor Moore, Robert L.
dc.contributor.advisor Trent, Tavan T.
dc.contributor.author Banjade, Debendra Prasad
dc.date.accessioned 2017-03-01T17:08:40Z
dc.date.available 2017-03-01T17:08:40Z
dc.date.issued 2014
dc.identifier.other u0015_0000001_0001575
dc.identifier.other Banjade_alatus_0004D_12023
dc.identifier.uri https://ir.ua.edu/handle/123456789/2031
dc.description Electronic Thesis or Dissertation
dc.description.abstract In 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.
dc.format.extent 83 p.
dc.format.medium electronic
dc.format.mimetype application/pdf
dc.language English
dc.language.iso en_US
dc.publisher University of Alabama Libraries
dc.relation.ispartof The University of Alabama Electronic Theses and Dissertations
dc.relation.ispartof The University of Alabama Libraries Digital Collections
dc.relation.hasversion born digital
dc.rights All rights reserved by the author unless otherwise indicated.
dc.subject.other Mathematics
dc.title Wolff's ideal problem in the multiplier algebra on dirichlet space
dc.type thesis
dc.type text
etdms.degree.department University of Alabama. Dept. of Mathematics
etdms.degree.discipline Mathematics
etdms.degree.grantor The University of Alabama
etdms.degree.level doctoral
etdms.degree.name Ph.D.

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