Hypergroups and their convolution algebras of multilinear forms

Mon, 02/06/2014 - 14:00

We will begin by introducing the notion of hypergroup, give some examples, 
and describe the convolution of measures on a hypergroup. After a review of 
some basic operator space theory, we shall describe how to extend the notion 
of convolution to the space of completely bounded multilinear forms on a cartesian 
product of spaces of continuous functions on hypergroups, thus making that space 
into a Banach algebra. When the hypergroups are commutative, we introduce and study 
a notion of Fourier transform in this setting.