On branching semi-groups, II

On Lie Semi-Groups

a subset of real Euclidean n-space, En, by (p, q) → F (p − q) = p ◦ q. In this note we shall be concerned with a representation T (.) of π as a semi-group of bounded linear operators on a Banach space X. More particularly, we suppose that postulates P1, P2, P3, P5, and P6 of chapter 25 of (2) are satisfied so that, by Theorem 25.3.1 of that book, there is a continuous function, f(.), defined on...

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

Semi-Groups Acting on Context-Free Graphs

Let ? be some context-free graph. We give suucient conditions on a semi-group of bisimulations H ensuring that the quotient Hn? is context-free. Using these suucient conditions we show that the quotient Aut(?)n? of ? by its full group of automorphisms is always context-free. We then give examples showing optimality (in some sense) of the above result.

Some Holomorphic Semi-groups.

W ∗ k = {x ǫX|xǫ Domain (A(a1) . . .A (ak)) for all a1, . . . , akǫA} is dense inX in theweak* topology. Let {e1, . . . , en} be a basis forA and setAi = A(ei), A ∗ i = A(ei). If α = (α1, . . . , αk), 1 ≤ αi ≤ n, is a sequence of integers we denote a product such as Aα1 . . .Aαk byAα; |α| = k is the length ofα. The operatorB ◦ = Σ|α|≤maαAα (the coefficients are complex numbers) is defined on Wm...

Semi-groups and Representations of Lie Groups

With every Lie semi-group, Π, possessing certain regularity properties, there is associated a Lie algebra, A; and with every strongly continuous representation of Π in a Banach space there is associated a representation A(a) of A. Certain theorems regarding this representation are established. The above theorems are valid for a representation of a Lie group also. In this case, it is shown that ...