Back to Departmental Colloquium: Fall 2006
Departmental Colloquium
Date: Thursday, Nov 16, 2006
Time: 4:15PM
Location: JWB 335
Francis Narcowich
Texas A&M University
Title |
Positive-weight quadrature and localized tight frames on Euclidean spheres. |
Abstract |
In this talk we will first discuss positive-weight quadrature formulas for the sphere that the author and co-workers have recently developed. We will also present a new class of frames on the sphere; these frames use these quadrature formulas. Frames resemble wavelets in many ways, and in fact are used in connection with them. Because there is no uniform grid on the sphere, it is not possible to construct direct analogues of, say, the Daubechies wavelets. Various types of wavelets for the sphere have been introduced, but all of them suffer from defects, such as poor localization properties and difficult implementation. Concerning the frames we discuss here, there are several novel features. They are tight, which makes reconstruction simple, and they have excellent localization properties. |
Applied Mathematics