Combinatorial and probabilistic techniques in harmonic analysis

dc.contributor.advisorVaaler, Jeffrey D.en
dc.contributor.committeeMemberBeckner, Williamen
dc.contributor.committeeMemberPavlovic, Natasaen
dc.contributor.committeeMemberRodriguez-Villegas, Fernandoen
dc.contributor.committeeMemberZuckerman, Daviden
dc.creatorLewko, Mark J., 1983-en
dc.date.accessioned2012-07-13T17:22:05Zen
dc.date.available2012-07-13T17:22:05Zen
dc.date.issued2012-05en
dc.date.submittedMay 2012en
dc.date.updated2012-07-13T17:22:12Zen
dc.descriptiontexten
dc.description.abstractWe prove several theorems in the intersection of harmonic analysis, combinatorics, probability and number theory. In the second section we use combinatorial methods to construct various sets with pathological combinatorial properties. In particular, we answer a question of P. Erdos and V. Sos regarding unions of Sidon sets. In the third section we use incidence bounds and bilinear methods to prove several new endpoint restriction estimates for the Paraboloid over finite fields. In the fourth and fifth sections we study a variational maximal operators associated to orthonormal systems. Here we use probabilistic techniques to construct well-behaved rearrangements and base changes. In the sixth section we apply our variational estimates to a problem in sieve theory. In the seventh section, motivated by applications to sieve theory, we disprove a maximal inequality related to multiplicative characters.en
dc.description.departmentMathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifier.slug2152/ETD-UT-2012-05-5531en
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2012-05-5531en
dc.language.isoengen
dc.subjectFourier analysisen
dc.subjectHarmonic analysisen
dc.subjectCombinatoricsen
dc.subjectNumber theoryen
dc.subjectProbabilityen
dc.titleCombinatorial and probabilistic techniques in harmonic analysisen
dc.type.genrethesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorUniversity of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen

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