Generalized wavelet transform on hypergroups

Let G be a locally compact hypergroup provided with a left Haar measure $$\mu $$ . Let K be a compact subhypergroup of G such that (G, K) is a Gelfand pair, and H be a locally compact group. In this paper, considering a continuous action of H on the dual space of G we define linear operators of wavelet type acting on square-integrable K-biinvariant functions on G and we study their ranges.