Bessel-type convolution algebras of bounded Borel measures on the matrix cones of positive semidefinite q×q-matrices over R,C,H were introduced recently by Rösler. These convolutions depend on some continuous parameter, generate commutative hypergroup structures and have Bessel functions of matrix argument as characters. Here, we first study the rich algebraic structure of these hypergroups. In...

In this paper we define ?-independent (a weak-version of independence), Kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and Sidon sets. These sets have the lacunarity or thinness property and are very useful indeed. For example Varopoulos used the Kronecker sets to prove the Malliavin theorem. In t...

In this paper we consider generalized moment functions of higher order. These are closely related to the well-known binomial type which have been investigated on various abstract structures. our former properties order commutative groups. particular, proved characterization a group as product an exponential and composition multivariate Bell polynomial sequence additive functions. present contin...

In this paper we introduce the smallest equivalence relation ξ∗ on a finite fuzzy hypergroup S such that the quotient group S/ξ∗, the set of all equivalence classes, is a solvable group. The characterization of solvable groups via strongly regular relation is investigated and several results on the topic are presented.

We investigate amenability and weak amenability of the l1-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, for the hypergroup induced by Chebyshev polynomials of the first kind we prove amenability.

in this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.we also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.

The theory of hyperstructures has been introduced byMarty in 1934 during the 8th Congress of the Scandinavian Mathematicians [4]. Marty introduced the notion of a hypergroup and since then many researchers have worked on this new topic of modern algebra and developed it. The notion of a hyperfield and a hyperring was studied first by Krasner [2] and then some authors followed him, for example, ...

measure always exists on a commutative hypergroup K, and there always exists a 'Plancherel measure' on the dual space K of equivalence classes of irreducible representations of K, with respect to which Plancherel's formula holds for Fourier transforms. In contrast with the case of a locally compact abelian group, however, the Plancherel measure is not necessarily a Haar measure on K, and K need...

This paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. The classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. Finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number