On Feller Semigroups Generated by Elliptic Operators with Integro-differential Boundary Conditions

摘要

In the 1950s, W. Feller gave a complete characterization of the analytic structure of one-dimensional diffusion processes [1, 2]. He proved that if an ordinary differential operator A is an infinitesimal generator of some contractive nonnegative semigroup, then a domain D(A) consists of functions satisfying integro-differential boundary conditions. Later such semigroups were called Feller semigroups. Conversely, if D(A) consists of functions with these nonlocal conditions, then A is an infinitesimal generator of some Feller semigroup.