Coorbit spaces related to locally compact hypergroups (Q682147)

The article studies the coorbit space \(S_{u,w}\) for a representation of a hypergroup \(K\) with admissible vector \(u\) and weight function \(w\) on \(K\). \(S_{u, w}\) carries a natural norm structure, under a condition on the weight \(w\), it is shown that \(S_{u, w}\) is complete - this condition is also shown to be necessary in certain situations. Examples of compact commutative hypergroups and the discrete hypergroup \(Z^+\) are discussed. There are also results on the independence of \(S_{u, w}\).