Luke G Rogers

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

    Authors: Robert S. Strichartz, Luke G Rogers, Alexander Teplyaev
    Subjects: Classical Analysis and ODEs
    Abstract

    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. The heat
    semigroup (probabilistic) method is applicable to a more general class of
    metric measure spaces with Laplacian, including certain infinitely ramified
    fractals, however the cut off technique involves some loss in smoothness. From
    the analytic approach we establish a Borel theorem for p.c.f.

RSS-материал