Contraction semigroups of elliptic quadratic differential operators

Elliptic operators generating stochastic semigroups

We use an intrinsic metric type approach to investigate when C0-semigroups generated by second order elliptic differential operators are stochastic. We give a new condition for stochasticity that encompasses the volume growth conditions by Karp and Li and by Perelmuter and Semenov. MSC 2000: 47D07, 35J15, 47B44

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Quantum dynamical semigroups generated by noncommutative unbounded elliptic operators

We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical semigroups for the generators and then use Chebotarev and Fagnola’s sufficient conditions for conservativity to show that the semigroups are conservative.

Trotter's Product Formula for Semigroups Generated by Quasilinear Elliptic Operators

Trotter's product formula is given for nonlinear semigroups in L1 (fi^) generated by quasilinear operators of the form Aic)}^t^h'u, where \ + ■ ■ ■ + in L'fr?^).

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...