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...

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...

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...

The DJ culture uses a gesture lexicon strongly rooted in the traditional setup of turntables and a mixer. As novel tools are introduced in the DJ community, this lexicon is adapted to the features they provide. In particular, multitouch technologies can offer a new syntax while still supporting the old lexicon, which is desired by DJs. We present a classification of DJ tools, from an interactio...

We present BeatJockey, a prototype interface which makes use of Audio Mosaicing (AM), beat-tracking and machine learning techniques, for supporting Diskjockeys (DJs) by proposing them new ways of interaction with the songs on the DJ’s playlist. This prototype introduces a new paradigm to DJing in which the user has the capability to mix songs interacting with beat-units that accompany the DJ’s ...

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.