(sg2) T(0)x = x for all x ∈ C; (sg3) T(s+ t) = T(s)◦T(t) for all s, t ≥ 0; (sg4) for each x ∈ C, the mapping t → T(t)x is continuous. We know that {T(t) : t ≥ 0} has a common fixed point under the assumption that C is weakly compact convex and E has the Opial property; see [3, 4, 5, 6, 8, 10, 12] and other works. Convergence theorems for one-parameter nonexpansive semigroups are proved in [1, 2...

The space-time dynamics generated by a system of reaction-diffusion equations in Rn on its global attractor are studied in this paper. To describe these dynamics the extended (n + 1)-parameter semigroup generated by the solution operator of the system and the n-parameter group of spatial translations is introduced and their dynamic properties are studied. In particular, several new dynamic char...

We show that the multiplication operator associated to a fractional power of a Gamma random variable, with parameter q > 0, maps the convex cone of the 1-invariant functions for a self-similar semigroup into the convex cone of the q-invariant functions for the associated Ornstein-Uhlenbeck (for short OU) semigroup. We also describe the harmonic functions for some other generalizations of the OU...

We consider the class of quantum mechanical master equations defined on a generic Banach space, arising by projecting weakly perturbed one-parameter groups of isometries. We show that the possible semigroup approximations are far from unique. However, uniqueness can be reestablished through the introduction of a dynamical time averaging map. The generator of the resulting Contraction Semigroup ...

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 ...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

An element d of a semigroup S is called divisible if it has roots of arbitrary order; that is, for every n ∈ N there is an element dn in S such that dn = d . If the elements dn can be taken in a prescribed subset D of S then d is said to be divisible in D . In the algebraic as well as in the topological theory of groups and semigroups divisibility is the major basic concept which allows the int...

This paper concerns the structure of strongly continuous one parameter semigroups of completely positive contractions of B(H) = B(K⊗L(0,∞)) which are intertwined by translation. These are called CP -flows over K. Using Bhat’s dilation result each unital CP -flow over K dilates to an Eo-semigroup of B(H1) where H1 can be considered to contain B(K⊗L(0,∞)). Every spatial Eo-semigroup is cocycle co...

1 Abstract. Let S ={si}i∈IN ⊆ IN be a numerical semigroup. For each i ∈ IN, let ν(si) denote the number of pairs (si−sj , sj) ∈ S: it is well-known that there exists an integer m such that the sequence {ν(si)}i∈IN is non-decreasing for i > m. The problem of finding m is solved only in special cases. By way of a suitable parameter t, we improve the known bounds for m and in several cases we dete...

We consider the standard model problem for a conical intersection of electronic surfaces in molecular dynamics. Our main result is the construction of a semigroup in order to approximate the Wigner function associated with the solution of the Schrödinger equation at leading order in the semiclassical parameter. The semigroup stems from an underlying Markov process which combines deterministic t...