If T = {T (t); t ≥ 0} is a strongly continuous family of bounded linear operators between two Banach spaces X and Y and f ∈ L1(0, b, X), the convolution of T with f is defined by (T ∗f)(t) = ∫ t 0 T (s)f(t− s)ds. It is shown that T ∗ f is continuously differentiable for all f ∈ C(0, b, X) if and only if T is of bounded semi-variation on [0, b]. Further T ∗ f is continuously differentiable for a...

The set of residue classes, modulo any positive integer, is commutative and associative under the operation of multiplication. The author made the conjecture: For each finite commutative semigroup, S, there exists a positive integer, n, such that S is isomorphic with a subsemigroup of the multiplicative semigroup of residue classes (mod n). (A semigroup is a set closed with respect to a single-...

We present a simple approach to study the one–dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space P 2 (R) of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of " sticky " particles, we obtain new explicit estimates of the solution in terms of the initial mass and momentum and we are able to construct an evol...

We present a simple approach to study the one–dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space P 2 (R) of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of " sticky " particles, we obtain new explicit estimates of the solution in terms of the initial mass and momentum and we are able to construct an evol...

let c be a field of subsets of a set i. also, let     1 i i be a non-decreasing positivesequence of real numbers such that 1, 1 0 1   i  and    11 i i . in this paper we prove thatbv of all the games of -bounded variation on c is a non-separable and norm dual banach space of thespace of simple games on c . we use this fact to establish the existence of a linear mapping t from...

This paper examines actions of right LCM semigroups by endomorphisms C*-algebras that encode an additional structure the semigroup. We define contractive covariant representations for these semigroup dynamical systems and prove a generalized Stinespring's dilation theorem showing can be dilated if only map on C*-algebra is unital completely positive. generalizes earlier results about dilations ...

Perturbations (r τt)t≥0 of the semigroup of shifts (τt)t≥0 on L(R+) are studied under the assumption that r τt−τt belongs to a certain Schatten–von Neumann class Sp with p ≥ 1. It is shown that, for the unitary component in the Wold– Kolmogorov decomposition of the cogenerator of the semigroup (r τt)t≥0, any singular spectral type may be achieved by S1-perturbations. An explicit construction is...

an array is said to converge to an element u when the ith marginal product converges to u\ an element is said to be infinitely divisible when it possesses a Jfeth root for each fee2. (A) There exists a continuous homomorphism A from the semigroup into the additive semigroup of nonnegative reals, such that A(u) = 0 if and only if u is the neutral element. (B) The set {u':u'\u} of factors of any ...