Uniform Semigroups Research Articles

The Structure of Regular Right Uniform Semigroups

In this paper, we investigate the right uniform notion on some classes of semigroups. The main objective of this paper is identifying the structure of regular right uniform semigroups which can be applied as a cornerstone of characterizing regular right subdirectly irreducible semigroups.

Uniform semigroup spectral analysis of the discrete, fractional and classical Fokker-Planck equations

In this paper, we investigate the spectral analysis (from the point of view of semi-groups) of discrete, fractional and classical Fokker-Planck equations. Discrete and fractional Fokker-Planck equations converge in some sense to the classical one. As a consequence, we first deal with discrete and classical Fokker-Planck equations in a same framework, proving uniform spectral estimates using a perturbation argument and an enlargement argument. Then, we do a similar analysis for fractional and classical Fokker-Planck equations using an argument of enlargement of the space in which the semigroup decays. We also handle another class of discrete Fokker-Planck equations which converge to the fractional Fokker-Planck one, we are also able to treat these equations in a same framework from the spectral analysis viewpoint, still with a semigroup approach and thanks to a perturbative argument combined with an enlargement one. Let us emphasize here that we improve the perturbative argument introduced in [7] and developed in [11], relaxing the hypothesis of the theorem, enlarging thus the class of operators which fulfills the assumptions required to apply it.

Product measures and convergence theorems for product integrals in integration theory for semigroup valued functions

In [11] Sion has investigated measures and integrals having values in uniform semigroups. In this paper a result which gives sufficient conditions for the existence of a unique product of semigroup valued measures is established. Moreover a convergence theorem for product integrals of semigroup valued functions is proved.

The support of a uniform semigroup valued measure

In this paper we introduce the notion of orthogonality for arbitrary families of elements of a partial abelian monoid, we study uniform semigroup valued measures on a partial abelian monoid, and we establish interesting results about the existence of the support of such measures.

Uniform semigroups and fixed point properties

LetS be a uniform semigroup (this includes all topological groups and affine semigroups). We show that a certain space of uniformly continuous functions onS has a left invariant mean iffS has the fixed point property for uniformly continuous affine actions ofS on compact convex sets. This is closely related to but independent of the results of T. Mitchell in [13] and A. Lau in [10]. Interesting examples and consequences are given for the special cases of topological groups and affine convolution semigroups of probability measures on a locally compact semigroup or group.

Uniform semigroups whose proper quasi-ideals are power joined

Uniform semigroups whose proper quasi-ideals are power joined

The Rees theorem for weakly uniform semigroups

The Rees theorem for weakly uniform semigroups

Quotients of uniform semigroups

Quotients of uniform semigroups