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 |