Fourier Transforms and the Delta Function

Dr. Kenneth Howell

Department of Mathematical Sciences
University of Alabama in Huntsville

March 19, 1999

Abstract

Fourier transforms and delta functions have long played major roles in applied analysis, especially in the study of differential equations. In this talk, we will briefly look at three basic approaches to these entities--the classical theory from ancient times (i.e., the 1800's and early 1900's), the classical theory of Laurent Schwartz (dating from the mid-1900's), and a relatively new (less than 10 years old theory) extending that of Schwartz and incorporating additional tools from complex analysis. The way newer theories build on older theories and address weaknesses in the older theories will be examined and partially illustrated through attempts to solve some relatively simple differential equations. If the speaker can talk fast enough, we will also discover some striking differences regarding the use of Taylor series in the two more modern theories.

This talk is mean for general (graduate and professional) audiences. It will be kept as simple as possible.