分野別セミナー

Abstact:
A relativistic stable process is a class of Levy process.
Its infinitesimal generator is related to the free relativistic
Hamiltonian.
In this talk, we discuss sharp two-sided estimates for the
transition densities of relativistic stable processes in
exterior open sets and half-space-like open sets for all time.
The estimates are uniform in mass m in the sense that the
constants are independent of m for small m.
As a corollary of our main result, we establish sharp two-sided
Green function estimates for relativistic stable processes with
mass $m\in (0, 1]$ in these open sets.
This talk is based on joint works with Zhen-Qing Chen and
Renming Song.