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Finite Pseudo-Differential Operators, Localization Operators for Curvelet and Ridgelet Transforms

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dc.contributor.advisorWong, Man Wah
dc.creatorLi, Jiawei
dc.date.accessioned2014-07-17T14:59:39Z
dc.date.available2014-07-17T14:59:39Z
dc.date.copyright2014-04-21
dc.date.issued2014-07-09
dc.date.updated2014-07-09T17:10:41Z
dc.degree.disciplineMathematics & Statistics
dc.degree.levelDoctoral
dc.degree.namePhD - Doctor of Philosophy
dc.description.abstractPseudo-differential operators can be built from the Fourier transform. However, besides the difficult problems in proving convergence and L^2-boundedness, the problem of finding eigenvalues is notoriously difficult. Finite analogs of pseudo-differential operators are desirable and indeed are constructed in this dissertation. Energized by the success of the Fourier transform and wavelet transforms, the last two decades saw the rapid developments of new tools in time-frequency analysis, such as ridgelet transforms and curvelet transforms, to deal with higher dimensional signals. Both curvelet transforms and ridgelet transforms give the time/position-frequency representations of signals that involve the interactions of translation, rotation and dilation, and they can be ideally used to represent signals and images with discontinuities lying on a curve such as images with edges. Given the resolution of the identity formulas for these two transforms, localization operators on them are constructed. The later part of this dissertation is to investigate the L^2-boundedness of the localization operators for curvelet transforms and ridgelet transforms, as well as their trace properties.en_US
dc.identifier.urihttp://hdl.handle.net/10315/27676
dc.language.isoenen_US
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectMathematicsen_US
dc.subject.keywordsWavelet Multipliersen_US
dc.subject.keywordsTime-Frequency Analysisen_US
dc.subject.keywordsLocalization Operatorsen_US
dc.subject.keywordsCurvelet Transformsen_US
dc.subject.keywordsRidgelet Transformsen_US
dc.subject.keywordsFinite Pseudo-Differential Operatorsen_US
dc.subject.keywordsHarmonic Analysisen_US
dc.subject.keywordsTrace Class Operatorsen_US
dc.titleFinite Pseudo-Differential Operators, Localization Operators for Curvelet and Ridgelet Transformsen_US
dc.typeElectronic Thesis or Dissertation

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