75 citations · 932 across the 61 of their papers we have counts for
4 papers · 1 filter
Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals
Benjamin Steinhurst, Alexander Teplyaev
We develop the foundation of the spectral analysis on Barlow-Evans projective limit fractals, or vermiculated spaces, which corresponds to symmetric Markov processes on these space…
Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals
Luke G Rogers, Robert S. Strichartz, 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 estimat…
Laplacians on the basilica Julia set
Luke G. Rogers, Alexander Teplyaev
We consider the basilica Julia set of the polynomial and construct all possible resistance (Dirichlet) forms, and the corresponding Laplacians, for which the topolog…
Calculus on the Sierpinski Gasket I: Polynomials, Exponentials and Power Series
Jonathan Needleman, Robert S. Strichartz, Alexander Teplyaev
We study the analog of power series expansions on the Sierpinski gasket, for analysis based on the Kigami Laplacian. The analog of polynomials are multiharmonic functions, which ha…