Energy measures and indices of Dirichlet forms, with applications to derivatives on some fractals
By M. Hino. 2009
73 citations recorded by the source corpus.
We introduce the concept of index for regular Dirichlet forms by means of energy measures, and discuss its properties. In particular, it is proved that the index of strong local regular Dirichlet forms is identical with the martingale dimension of the associated diffusion processes. As an application, a class of self‐similar fractals is taken up as an underlying space. We prove that first‐order derivatives can be defined for functions in the domain of the Dirichlet forms and their total energies are represented as the square integrals of the derivatives.
Subfields: Condensed Matter Physics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/beb31368206b13a50008a404829abd307d721a5b
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In Condensed Matter Physics
In Mathematical Physics
- Naotaka Kajino
- Michael Hinz
- Alexander Teplyaev
- Michael Röckner
- Wei Liu
- Tusheng Zhang
- Vladimir Bogachev
- Giuseppe Da Prato
Citations in the corpus
- Heat Kernel Asymptotics for the Measurable Riemannian Structure on the Sierpinski Gasket (2012, background): “We follow mainly [25] for the presentation of this section, but we sometimes refer to also [17,22,23,26,29] for related facts.”
- Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces (2012, methodology): “of functions admitting energy densities and being energy dense in the space of bounded energy finite functions. Switching to a suitable measure if needed (called an energy dominant or Kusuoka measure, [22, 47]), this can be realized for any local regular Dirichlet form. Following [13] we therefore ob”