Regular subspaces of regular Dirichlet forms

Quasi-Regular Dirichlet Forms and Applications

Since the celebrated result of Fukushima on the connection between regular Dirichlet forms and Hunt processes in 1971, the theory of Dirichlet forms has been rapidly developed and has brought a wide range of applications in various related areas of mathematics and physics (see e.g. the three new books [BH 91], [MR 92], [FOT 94] and references therein). In this survey paper I shall mainly discus...

Quasi-regular Dirichlet forms: Examples and counterexamples

We prove some new results on quasi-regular Dirichlet forms. These include results on perturbations of Dirichlet forms, change of speed measure, and tightness. The tightness implies the existence of an associated right continuous strong Markov process. We also discuss applications to a number of examples including cases with possibly degenerate (sub)-elliptic part, diffusions on loops spaces, an...

Quasi-regular topologies for L-resolvents and semi-Dirichlet forms

We prove that for any semi-Dirichlet form (ε, D(ε)) on a measurable Lusin space E there exists a Lusin topology with the given σ-algebra as the Borel σ-algebra so that (ε, D(ε)) becomes quasi–regular. However one has to enlarge E by a zero set. More generally a corresponding result for arbitrary L-resolvents is proven.

Five regular or nearly-regular ternary quadratic forms

Strictly regular ternary Hermitian forms

Article history: Received 28 October 2015 Received in revised form 8 April 2016 Accepted 9 April 2016 Communicated by David Goss MSC: primary 11E39 secondary 11E12, 11E20