Harmonic Analysis and Differential Equations Seminar: George Bayliss (UIUC)

Speaker:  George Bayliss (UIUC)

Participants are invited to lunch beforehand with the speaker at the Bread Company at 12:00pm

Title: The Evans function as a bound on spectral distance

Abstract: The Evans function is an analytic function associated with a boundary value problem whose roots (and their multiplicity) correspond exactly to the eigenvalues of the problem. As such, one often views the Evans function as binary, either zero or nonzero at a particular point. In this talk I will demonstrate that, for a variety of problems on a compact interval, there is an easily computable scaling of the Evans function so that at any element of the resolvent set its value is a lower bound on the distance to the nearest eigenvalue. I will note some properties of this scaling, discuss the extension to multiple spectral parameters, and show some computations.