Hypergroups and their convolution algebras of multilinear forms
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.