ON DUAL GENERATORS FOR NON-LOCAL SEMI-DIRICHLET FORMS
Toshihiro Uemura
Abstract: Let be a measurable function defined on off the diagonal, where
is a locally compact separable metric space, and let be a positive Radon measure on
with full support. In 2012, we showed that a quadratic form having as a
Lévy kernel becomes a lower bounded semi-Dirichlet form on which is
non-local and regular. Then there associates a Hunt process corresponding to the
semi-Dirichlet form. In the case where , we will show that the dual form of the
semi-Dirichlet form also produces a Hunt process by taking a killing. As a byproduct, a
precise description of the infinitesimal generator of the dual form is also given.