The Uncertainty Principle in Harmonic Analysis and Bourgain's Theorem

Loading...
Thumbnail Image
Files
Powell.pdf(376.54 KB)
No. of downloads: 180
Publication or External Link
Date
2003
Authors
Powell, Alexander M.
Advisor
Benedetto, John J.
Citation
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.
Notes
Rights