Self-similar Energies On Finitely Ramified Fractals

This monograph delves into the theory of self-similar energies on finitely ramified self-similar fractals. Using these self-similar energies, one can construct Laplacians, harmonic functions, Brownian motion, and differential equations specific to these fractals.

On finitely ramified fractals, self-similar energies are derived from eigenforms — quadratic forms that are eigenvectors of a special nonlinear operator within a finite-dimensional function space. The monograph also explores …