Convergence of positive operator semigroups

Operator Semigroups for Convergence Analysis

The paper serves as a review on the basic results showing how functional analytic tools have been applied in numerical analysis. It deals with abstract Cauchy problems and present how their solutions are approximated by using space and time discretisations. To this end we introduce and apply the basic notions of operator semigroup theory. The convergence is analysed through the famous theorems ...

A General Theorem on the Convergence of Operator Semigroups

In all of these theorems the notion of convergence used in (1-1) and (1-2) has essentially been strong convergence. It is the purpose of the present paper to prove analogous theorems for a certain class of notions of convergence, which will include, in the case of Banach spaces of functions with the sup norm, bounded, pointwise convergence, and convergence of bounded sequences which is uniform ...

Connexion with Operator Semigroups

On supermatrix idempotent operator semigroups

One-parameter semigroups of antitriangle idempotent supermatrices and corresponding superoperator semigroups are introduced and investigated. It is shown that t-linear idempotent superoperators and exponential superoperators are mutually dual in some sense, and the first gives additional to exponential solution to the initial Cauchy problem. The corresponding functional equation and analog of r...

Applications of Operator Semigroups To Fourier

Dedicated to the memory of Al Cliiord, a wonderful mathematician and a wonderful man. Abstract Of concern are semigroups of linear norm one operators on Hilbert space of the form (discrete case) T = fT n : n = 0; 1; 2; g or (continuous case) T = fT (t) : t 0g: Using ergodic theory and Hilbert-Schmidt operators, the Cess aro limits (as n! 1) of j< T n f; f >j 2 ; j< T (n)f; f >j 2 are computed (...