Colloquium

Speaker: Prof. Alexander Powell (Vanderbilt University)
Title: Means and variances of bases and the uncertainty principle
Time: 2013-07-25 (Thu.)  15:00 - 16:00
Place:
Abstract: The classical uncertainty principle in harmonic analysis is the general statement that an individual function and its Fourier transform cannot be simultaneously too well-localized. In this talk, we shall discuss versions of the uncertainty principle that constrain the collective time-frequency localization of orthonormal bases and other spanning systems. For example, we shall discuss a question of H. Shapiro concerning geometric aspects of how bases "cover" information in the time-frequency plane. We shall also discuss versions of the Balian-Low uncertainty principle for Gabor systems. A Gabor system is a collection of functions that is formed by translations and modulations of a fixed window function (analogous to the translation-dilation structure in wavelets). The Balian-Low theorem describes trade-offs between different types of spanning structure and time-frequency localization of Gabor systems.
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