Jack Arbunich : Oscillatory Integrals of the First Kind

Posted by Trevor Leslie , part of the Graduate Analysis Seminar.

At

Sept. 26, 2016, noon

In

SEO 1227

Abstract

Oscillatory integrals have been an integral part of Harmonic analysis from its conception. The Fourier transform is a ripe example of such an oscillatory integral. One main use of oscillatory integrals is to obtain decay estimates for Fourier transforms of measures on surfaces. In a sense, oscillatory integrals link geometric properties of manifolds and the harmonic analysis related to them. We will prove a few basic yet noteworthy results on the asymptotics of oscillatory integrals in 1D.