A difference of composition operators on Bergman space

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dc.contributorMoen, Kabe
dc.contributorWu, Zhijian
dc.contributorMoore, Robert L.
dc.contributorXiao, Yang
dc.contributorWang, James L.
dc.contributor.advisorMoen, Kabe
dc.contributor.advisorWu, Zhijian
dc.contributor.authorAcharyya, Soumyadip
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2017-03-01T17:35:51Z
dc.date.available2017-03-01T17:35:51Z
dc.date.issued2015
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractLet us consider the operator-theoretic difference of two composition operators acting on a weighted Hilbert Bergman space. In 2011, Choe , Hosokawa and Koo [CHK] proved a necessary and sufficient condition under which the difference operator is Hilbert-Schmidt. In this dissertation, we have provided a simpler proof of their result , using a change of variable method. Applying that method, we have also established similar necessary and sufficient integral condition under which a difference operator of a more general form is Hilbert-Schmidt. In 2011, Saukko [S] found a beautiful way of characterizing the boundedness and compactness of the difference of two composition operators , acting in between two weighted Bergman spaces. More precisely, he was able to reduce those problems for a difference operator into corresponding problems for a weighted composition operator, which were already solved in the year 2007. In this work, we have generalized Saukko's results for the same operator where the target function space is more general. Through these generalized results, we have been able to characterize the boundedness and compactness of the previously mentioned difference operator with a more general form.en_US
dc.format.extent74 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0001992
dc.identifier.otherAcharyya_alatus_0004D_12417
dc.identifier.urihttps://ir.ua.edu/handle/123456789/2397
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.titleA difference of composition operators on Bergman 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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