This paper investigates the question of when a finite hypergroup with three elements is strong, that is satisfies the condition that its dual signed hypergroup is actually a hypergroup. We classify hermitian hypergroups of order three by weight into two dimensional families and show that the algebraic conditions arising from duality yield four interesting curves in the plane which bound the cha...

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...

It is well known that finite commutative association schemes in the sense of the monograph of Bannai and Ito lead to finite commutative hypergroups with positive dual convolutions and even dual hypergroup structures. In this paper we present several discrete generalizations of association schemes which also lead to associated hypergroups. We show that discrete commutative hypergroups associated...

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 using strongly duplexes we introduce a new class of (semi)hypergroups. The associated (semi)hypergroup from a strongly duplex is called duplex (semi)hypergroup. Two computer programs written in MATLAB show that the two groups Z2n and Zn × Z2 produce a strongly duplex and its associated hypergroup is a complementary feasible hypergroup.

Let K be a locally compact hypergroup. In this paper we initiate the concept of fundamental domain in locally compact hypergroups and then we introduce the Borel section mapping. In fact, a fundamental domain is a subset of a hypergroup K including a unique element from each cosets, and the Borel section mapping is a function which corresponds to any coset, the related unique element in the fun...

Let X be a hypergroup. In this paper, we define a locally convex topology β on L(X) such that (L(X), β) with the strong topology can be identified with a Banach subspace of L(X). We prove that if X has a Haar measure, then the dual to this subspace is LC(X) ∗∗ = cl{F ∈ L(X);F has compact carrier}. Moreover, we study the operators on L(X) and L 0 (X) which commute with translations and convoluti...