The objects of the present study are one-parameter semigroups generated by Schrödinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the Kato class and impose on the vector potentials only local Kato-like conditions. The configuration space is supposed to be an arbitrary open subset of multidimensional Euclidean space; in case that it ...

We use a monotone iterative method in the presence of lower and upper solutions to discuss the existence and uniqueness of mild solutions for the initial value problem u′(t) + Au(t) = f(t, u(t), Tu(t)), t ∈ J, t 6= tk, ∆u|t=tk = Ik(u(tk)), k = 1, 2, . . . , m, u(0) = x0, where A : D(A) ⊂ E → E is a closed linear operator and −A generates a strongly continuous semigroup T (t)(t ≥ 0) in E. Under ...

We consider a class of non-trivial perturbations A of the degenerate OrnsteinUhlenbeck operator in R . In fact we perturb both the diffusion and the drift part of the operator (say Q and B) allowing the diffusion part to be unbounded in R . Assuming that the kernel of the matrix Q(x) is invariant with respect to x ∈ R and the Kalman rank condition is satisfied at any x ∈ R by the same m < N , a...

in the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup s with a weight function w into a proper h*-algebra a in terms of w-bounded continuous positive definite a-valued functions on s. a generalization of a well-known result of k. harzallah is obtained. an earlier conjecture of the author ...

Consider a semigroup action on a set. We derive conditions, in terms of the induced action of the semigroup on {0, 1}-valued probability charges, which ensure that all invariant probability charges are strongly continuous.

We show that any Hermiticity and trace preserving continuous semigroup {γt}t>0 in d dimensions is completely positive if and only if the semigroup {γt⊗ γt}t>0 is positivity preserving.