MATHEMATICS COLLOQUIUM

presents

**Gilbert G. Walter
**Professor Emeritus

Department of Mathematical Sciences

University of Wisconsin-Milwaukee

*Chromatic Series of Prolate Spheroidal Waves*

Abstract:

Chromatic series constitute an alternative to Taylor series which work better for band-limited functions. They are based on orthogonal polynomials which however do not have optimum local properties. In this work, we replace the polynomials with another orthogonal series based on the prolate spheroidal wave functions. These functions are band-limited and have the maximum energy on a given interval. An alternate version of the chromatic series is based on wavelet series arising from these functions.