Explicit formulas for heat kernels on diamond fractals

Patricia Alonso Ruiz

Published 2017-12-01Version 1

This paper provides an explicit pointwise formula for the heat kernel on compact metric spaces that belong to a $(\mathbb{N}\times\mathbb{N})$-parameter family of fractals which are regarded as projective limits of metric measure graphs and do not satisfy the volume doubling property. The formulas are applied to obtain uniform continuity estimates of the heat kernel and to derive an expression of the fundamental solution of the free Schr\"odinger equation. The results also open up the possibility to approach infinite dimensional spaces based on this model.