Harmonic analysis on a locally compact hypergroup - Kalyuzhnyi, A. A.; Podkolzin, G. B.; Chapovsky, Yu. A. (Methods of Functional Analysis and Topology, 2010)
We propose a new axiomatics for a locally compact hypergroup. On the one hand, the new object generalizes a DJS-hypergroup and, on the other hand, it allows to obtain results similar to those for a unimodular hypecomplex system with continuous basis. We construct a harmonic analysis and, for a commutative locally compact hypergroup, give an analogue of the Pontryagin duality theorem.