Mean Value Properties of Harmonic Functions on Sierpinski Gasket Type Fractals

Sampling on the Sierpinski Gasket

Boundary Value Problems on a Half Sierpinski Gasket

We study boundary value problems for the Laplacian on a domain Ω consisting of the left half of the Sierpinski Gasket (SG), whose boundary is essentially a countable set of points X. For harmonic functions we give an explicit Poisson integral formula to recover the function from its boundary values, and characterize those that correspond to functions of finite energy. We give an explicit Dirich...

Invariant Mean Value Property and Harmonic Functions

We give conditions on the functions σ and u on R such that if u is given by the convolution of σ and u, then u is harmonic on R.

Harmonic functions via restricted mean-value theorems

Let f be a function on a bounded domain Ω ⊆ R and δ be a positive function on Ω such that B(x, δ(x)) ⊆ Ω. Let σ(f)(x) be the average of f over the ball B(x, δ(x)). The restricted mean-value theorems discuss the conditions on f, δ, and Ω under which σ(f) = f implies that f is harmonic. In this paper, we study the stability of harmonic functions with respect to the map σ. One expects that, in gen...

Random walks on the Sierpinski Gasket

The generating functions for random walks on the Sierpinski gasket are computed. For closed walks, we investigate the dependence of these functions on location and the bare hopping parameter. They are continuous on the infinite gasket but not differentiable. J. Physique 47 (1986) 1663-1669 OCTOBRE 1986, Classification Physics Abstracts 05.40 05.50 1. Preliminaries and review of known results. C...