COLLOQUIUM
Widder’s Theorem for
Dirichlet Spaces
Dr. Nate Eldredge
Visiting Assistant Professor
Cornell University
Abstract
One of the simplest partial differential equations is the heat
equation in Rⁿ, used to model heat flow and particle diffusion. A
natural question about this model is whether solutions of the heat
equation are uniquely determined by their initial conditions. In
general, the answer is no, but a classical theorem of D. Widder
gives a positive answer for nonnegative solutions. I will discuss
this problem, giving some background on the heat equation and its
connection to Brownian motion. I will then describe some recent
work extending Widder’s result to the more general context of
Dirichlet spaces, whose geometry can be quite pathological.
Department of
Mathematics
Wednesday,
March 7th, 2012
4:00 p.m.
204 Morgan Hall
Refreshments will be
served at 3:45 p.m.