Month: September 2009

Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals.

by Luke G. Rogers, Robert S. Strichartz and Alexander Teplyaev

We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth
functions on fractals, one using a probabilistic approach and sub-Gaussian estimates for the heat
operator, and the other using the analytic theory for p.c.f. fractals and a fixed point argument. Continue reading