Analysis on Graphs and Fractals

Distributions on p.c.f. Fractafolds

L Rogers, Cornell University, USA

Abstract

I will talk about joint work with Strichartz in which we produce a theory of distributions on fractafolds based on a p.c.f. fractal.  In particular we are able to prove analogues of the classical structure theorems, which identify distributions (locally) as powers of the Laplacian applied to continuous functions, and show that distributions of point support are "derivatives" of Dirac masses.