THE UNCERTAINTY PRINCIPLE IN HARMONIC ANALYSIS AND BOURGAIN'S THEOREM
| dc.contributor.advisor | Powell, Alexander M. | |
| dc.contributor.author | Benedetto, John J. | |
| 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 | 2019-09-25T16:59:35Z | |
| dc.date.available | 2019-09-25T16:59:35Z | |
| 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/j3tv-tjfx | |
| dc.identifier.uri | http://hdl.handle.net/1903/24913 | |
| 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 |