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...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

Nuclearity of the Hankel operator is a known sufficient condition for convergence of Lyapunov-balanced truncations. We show how a previous result on nuclearity of Hankel operators of systems with an analytic semigroup can be extended to systems with a semigroup of class D with p ≥ 1 (the case p = 1 being the analytic case). For semigroups that are generated by a Dunford-Schwartz spectral operat...

We study the anti-periodic problem for the semilinear partial neutral evolution equation in the form d dt [u(t) + h(t, u(t))] + Au(t) = f(t, u(t)), t ∈ R in a Banach space X, where h, f are given X-valued functions, and −A : D(A) ⊆ X → X is the infinitesimal generator of a compact analytic semigroup. Some new theorems concerning the existence of anti-periodic mild solutions for the problem are ...

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...

We consider perturbations of dynamical semigroups on the algebra all bounded operators in a Hilbert space generated by covariant completely positive measures semi-axis. The construction is based upon unbounded linear generators preadjoint nuclear operators. As an application we construct perturbation semigroup non-unital *-endomorphisms canonical anticommutation relations resulting flow shifts.

Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we prove conditions ensuring that a ...