in [1,2,3], a. c. baker and j.w. baker studied the subspace ma(s) of the convolution measure algebra m, (s) of a locally compact semigroup. h. dzinotyiweyi in [5,7] considers an analogous measure space on a large class of c-distinguished topological semigroups containing all completely regular topological semigroups. in this paper, we extend the definitions to study the weighted semigroup algeb...

Let S be a locally compact topological foundation semigroup with identity and Ma(S) be its semigroup algebra. In this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $M_a(S)$ of a locally compact topological foundationsemigroup with identity.

In a recent work we have found a contraction semigroup able to correctly approximate a projected and perturbed one-parameter group of isometries in a generic Banach space, in the limit of weak-coupling. Here we study its generator by specializing toW ∗-algebras: after defining a Physical Subsystem in terms of a completely positive projecting conditional expectation, we find that it generates a ...

This paper proposes a general algebraic construction technique for image scale-spaces. The basic idea is to rst downscale the image by some factor using an invertible scaling, then apply an image operator (linear or morphological) at a unit scale, and nally resize the image to its original scale. It is then required that the resulting one-parameter family of image operators satis es the semigro...

Let T (t), 0 ≤ t < ∞, be a one parameter c0-semigroup of bounded linear operators on a Banach space X with infinitesimal generator A and R(λ, A) be the resolvent operator of A. The Hille-Yosida Theorem for c0-semigroups asserts that the resolvent operator of the infinitesimal generator A satisfies ‖R(λ, A)‖ ≤ M λ−ω for some constants M > 0 and λ ∈ R (the set of real numbers), λ > ω. The object ...

We obtain a generalization of the Burns-Krantz rigidity theorem for holomorphic self-mappings of the unit disk in the spirit of the classical Schwarz-Pick Lemma and its continuous version due to L.Harris via the generation theory for one-parameter semigroups. In particular, we establish geometric and analytic criteria for a holomorphic function on the disk with a boundary null point to be a gen...

This paper proposes a general algebraic construction technique for image scale-spaces. The basic idea is to rst downscale the image by some factor using an invertible scaling, then apply an image operator (linear or morphological) at a unit scale, and nally resize the image to its original scale. It is then required that the resulting one-parameter family of image operators satisses the semigro...

By suitably extending a Feynman-Kac formula of Simon [Canadian Math. Soc. Conf. Proc. 28, 317–321 (2000)], we study one-parameter semigroups generated by (the negative of) rather general Schrödinger operators, which may be unbounded from below and include a magnetic vector potential. In particular, a common domain of essential self-adjointness for such a semigroup is specified. Moreover, each m...

A classical theory is developed for the time development and scattering of a minimally coupled scalar eld on closed spacetimes that evolve from initial, to nal static states. The time development is obtained by reformulating the eld equation as an abstract Cauchy problem on a Hilbert space. Constraints are imposed on the metric that enable the use of semigroup theory, and the eld solution is ob...

Let ~ C be a category whose objects are semigroups with topology and morphisms are closed semigroup relations, in particular, continuous homomorphisms. An object X of the category ~ C is called ~ C-closed if for each morphism Φ ⊂ X×Y in the category ~ C the image Φ(X) = {y ∈ Y : ∃x ∈ X (x, y) ∈ Φ} is closed in Y. In the paper we survey existing and new results on topological groups, which are ~...