Title: The Feller Semigroups
Speaker: A. L. Skubachevskii
Speaker Info: Moscow, Russia
Brief Description:
Special Note:
Abstract:
In 50s W.Feller considered the following problem arising in biophysics. Let a second order ordinary differential operator be a generator of a nonnegative contractive semigroup (so-called Feller semigroup). What can we say about a domain of this operator? W.Feller has proved that this domain consists of functions satisfying nonlocal boundary conditions including the integrals over some Borel measure. Conversily, he has proved that if a second order ordinary differential operator has such domain, then it is a generator of a Feller semigroup. In 1959 A.D.Ventsel has proved that if a second order elliptic operator is a generator of a Feller semigroup, then a domain of such operator consists of functions satisfying some nonlocal boundary conditions. The inverse statement was proved only in some particular cases. We shall formulate the sufficient conditions of existence of Feller semigroups. It will be also constructed counterexamples, which show that these coditions are essential.Date: Monday, November 17, 2008