A categorical approach to operator semigroups

Connexion with Operator Semigroups

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 (...

On minimal realization of IF-languages: A categorical approach

he purpose of this work is to introduce and study the concept of minimal deterministic automaton with IF-outputs which realizes the given IF-language. Among two methods for construction of such automaton presented here, one is based on Myhill-Nerode's theory while the other is based on derivatives of the given IF-language. Meanwhile, the categories of deterministic automata with IF-outputs and ...

A Categorical Approach to Integration

We present a general treatment of measures and integrals in certain (monoidal closed) categories. Under appropriate conditions the integral can be defined by a universal property, and the universal measure is at the same time a universal multiplicative measure. In the multiplicative case this assignment is right adjoint to the formation of the Boolean algebra of idempotents. Now coproduct prese...

A Categorical Approach to Convergence

We define the concept of a convergence class on an object of a given category by using certain generalized nets for expressing the convergence. The resulting topological category, whose objects are the pairs consisting of objects of the original category and convergence classes on them, is then investigated. We study the full subcategories of this category which are obtained by imposing on it s...