When

Start: 02/08/2016 - 4:15pm

End : 02/08/2016 - 5:15pm

End : 02/08/2016 - 5:15pm

Category

Applied Math Seminar

Speaker

Charles K. Chui (Department of Statistics, Stanford University)

Abstract

The strategy of divide-and-conquer applies to just about all scientific and engineering disciplines for theoretical and algorithmic development as well as experimental implementations for various applications. In mathematics, perhaps one of the most exciting theoretical development in this direction is the notion of “atomic decomposition” for the Hardy spaces $H^p(\R)$ with $0<p\le1$, introduced by Raphy Coifman in a 1974 paper, which contributed to motivate his joint work with Yves Meyer and Elias Stein, published some 10 years later, on the introduction and characterization of the so-called Tent spaces. This significant piece of work has important applications to the unification and simplification of the basic techniques in harmonic analysis. Furthermore, the atomic decomposition of these and other function spaces, contributed by others, has profound impact to the advancement of both harmonic and functional analyses over the decades of the 80’s and 90’s. An important property of Coifman’s atoms for $H^p(\R)$, with $0<p\le1$, is their vanishing moments of order up to $1/p$, leading to the introduction of wavelets and the rapid advances of wavelet analysis and algorithmic development, with applications to most engineering and physical science disciplines for a duration of over two decades.

In a recent joint paper with Hrushikesh Mhaskar and my student, Maria van der Walt, of Vanderbilt University, we have initiated a study of the construction of atoms for signal decomposition directly from the input signal itself. The objective of this seminar is to discuss the background of our approach, compare our results with the state-of-the-arts, and conclude the presentation with a brief discussion our computational scheme to signal extrapolation.

Where

Emmy Noether Room
Millikan 1021 Pomona College

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