Hypergroup structures arising from certain dual objects of a hypergroup

Convolution operators on the dual of hypergroup algebras

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...

The L-fuzzy Nakano hypergroup

In this paper we start with a lattice (X,∨,∧) and define, in terms of ∨, a family of crisp hyperoperations tp (one hyperoperation for each p ∈ X). We show that, for every p, the hyperalgebra (X,tp) is a join space and the hyperalgebra (X,tp,∧) is very similar to a hyperlattice. Then we use the hyperoperations tp as p-cuts to introduce an L-fuzzy hyperoperation t and show that (X,t) is an L-fuzz...

Random walks on hypergroup of conics in finite fields

In this paper we study random walks on the hypergroup of conics in finite fields. We investigate the behavior of random walks on this hypergroup, the equilibrium distribution and the mixing times. We use the coupling method to show that the mixing time of random walks on hypergroup of conics is only linear. Mathematics Subject Classifications: 60D05, 11A99. Keywoords: random walks, hypergroups,...

Littlewood-Paley g-Functions and Multipliers for the Laguerre Hypergroup

Multiresolution Analysis and Haar Wavelets on the Laguerre Hypergroup

In the past decade research on the multiresolution analysis has made considerable progress due to its wide applications. For the basic theory of multiresolution we refer readers to the work in 1, 2 . Recently, we find that a lot of authors try to extend the theory of wavelets on the Euclidean space to nilpotent Lie groups see 3–6 . In this paper we will give the definition of acceptable dilatio...