The Uncertainty Principle in Harmonic Analysis and Bourgain's Theorem

dc.contributor.advisor	Benedetto, John J.
dc.contributor.author	Powell, Alexander M.
dc.contributor.department	Mathematics
dc.contributor.publisher	Digital Repository at the University of Maryland
dc.contributor.publisher	University of Maryland (College Park, Md)
dc.date.accessioned	2018-07-17T15:39:56Z
dc.date.available	2018-07-17T15:39:56Z
dc.date.issued	2003
dc.description.abstract	We investigate the uncertainty principle in harmonic analysis and how it constrains the uniform localization properties of orthonormal bases. Our main result generalizes a theorem of Bourgain to construct orthonormal bases which are uniformly well-localized in time and frequency with respect to certain generalized variances. In a related result, we calculate generalized variances of orthonormalized Gabor systems. We also answer some interesting cases of a question of H. S. Shapiro on the distribution of time and frequency means and variances for orthonormal bases.	en_US
dc.identifier	https://doi.org/10.13016/M27D2QB3B
dc.identifier.uri	http://hdl.handle.net/1903/21087
dc.language.iso	en_US	en_US
dc.title	The Uncertainty Principle in Harmonic Analysis and Bourgain's Theorem	en_US
dc.type	Dissertation	en_US

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