Absolutely continuous functions on idempotent semigroups in the locally convex setting

Functions of bounded variation on idempotent semigroups

Free profinite locally idempotent and locally commutative semigroups

This paper is concerned with the structure of semigroups of implicit operations on the pseudovariety LSl of finite locally idempotent and locally commutative semigroups. We depart from a general result of Almeida and Weil to give two descriptions of these semigroups: the first in terms of infinite words, and the second in terms of infinite and bi-infinite words. We then derive some applications...

Idempotent Measures on Compact Semigroups

Throughout this paper, 5 will be a compact Hausdorff topological semigroup, 5 will denote the convolution semigroup of normalized non-negative regular Borel measures on 5, and H will be the carrier of a measure p in 5. The space of continuous complex valued functions on 5 will be denoted by C(S), while Cr(S) will be the subspace of C(S) of real valued functions. Standard terminology and definit...

The join of the pseudovarieties of idempotent semigroups and locally trivial semigroups

This article solves a problem proposed by Almeida: the computation of the join of two well-known pseudovarieties of semigroups, namely the pseudovariety of bands and the pseudovariety of locally trivial semigroups. We use a method developed by Almeida, based on the theory of implicit operations.

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...