Explicit Formulas for Heat Kernels on Diamond Fractals
Abstract
This paper provides explicit pointwise formulas for the heat kernel on compact metric measure spaces that belong to a ({N×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 Schrödinger equation. The results also open up the possibility to approach infinite dimensional spaces based on this model.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 December 2018
 DOI:
 10.1007/s002200183221x
 arXiv:
 arXiv:1712.00385
 Bibcode:
 2018CMaPh.364.1305A
 Keywords:

 Mathematics  Probability;
 35K08;
 60J60;
 81Q35;
 35C10;
 31C25;
 28A80
 EPrint:
 19 pages, 7 figures