Explicit Formulas for Heat Kernels on Diamond Fractals Academic Article uri icon

abstract

  • This paper provides explicit pointwise formulas for the heat kernel on compact metric measure spaces that belong to a $(mathbb{N} imesmathbb{N})$-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.

published proceedings

  • COMMUNICATIONS IN MATHEMATICAL PHYSICS

altmetric score

  • 0.75

author list (cited authors)

  • Ruiz, P. A.

citation count

  • 16

complete list of authors

  • Ruiz, Patricia Alonso

publication date

  • August 2018