The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

We consider a frequency localized Bernstein inequality for the fractional Laplacian operator, which has wide applications in fluid dynamics such as dissipative surface quasi-geostrophic equations. We use a heat flow reformulation and prove the inequality for the full range of parameters and in all dimensions. A crucial observation is that after frequency projection the zeroth frequency part of ...

Proper extensions that are “injective on L-related idempotents” of R-unipotent semigroups, and much more generally of the class of generalised left restriction semigroups possessing the ample and congruence conditions, referred to here as glrac semigroups, are described as certain subalgebras of a λ-semidirect product of a left regular band by an R-unipotent or by a glrac semigroup, respectivel...

We consider solutions of affine stochastic functional differential equations on R. The drift of these equations is specified by a functional defined on a general function space B which is only described axiomatically. The solutions are reformulated as stochastic processes in the space B. By representing such a process in the bidual space of B we establish that the transition functions of this p...

The concept of an automatic structure has been generalized from groups [ECH+] to semigroups [CRRT]. Several authors [CRR, Hof, Kam] have asked the following question: Let S be a finitely generated semigroup embeddable in a group and let G be its universal group [CP, Chapter ]. If G is automatic, must S be automatic? Examples in favour of this implication include: free groups and s...

Let K be a nonempty subset of a p-uniformly convex Banach space E, G a left reversible semitopological semigroup, and = {Tt : t ∈G} a generalized Lipschitzian semigroup of K into itself, that is, for s ∈ G, ‖Tsx−Tsy‖ ≤ as‖x−y‖+bs(‖x−Tsx‖+ ‖y−Tsy‖)+cs(‖x−Tsy‖+‖y−Tsx‖), for x,y ∈ K where as,bs ,cs > 0 such that there exists a t1 ∈ G such that bs +cs < 1 for all s t1. It is proved that if there ex...

We give three proofs of a functional inequality for the standard Gaussian measure originally due to William Beckner. The first uses the central limit theorem and a tensorial property of the inequality. The second uses the Ornstein-Uhlenbeck semigroup, and the third uses the heat semigroup. These latter two proofs yield a more general inequality than the one Beckner originally proved. We then ge...

In this work, we aim to prove algebra properties for generalized Sobolev spaces W ∩L on a Riemannian manifold, whereW s,p is of Bessel-typeW s,p := (1+L)(L) with an operator L generating a heat semigroup satisfying off-diagonal decays. We don’t require any assumption on the gradient of the semigroup. To do that, we propose two different approaches (one by a new kind of paraproducts and another ...

This paper studies FA-presentable structures and gives a complete classification of the finitely generated FA-presentable cancellative semigroups. We show that a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group.