We describe an infinitesimal algebra to a hypergroup constructed from a Lie group and a conditional expectation. We also prove a theorem on a decomposition of the conditional expectation into the product of a counital conditional expectation and the one that arises in the double coset construction.

Harmonic analysis on a locally compact hypergroup

A. A. Kalyuzhnyi, G. B. Podkolzin, Yu. A. Chapovsky

↓ Abstract | Article (.pdf)

MFAT 16 (2010), no. 4, 304-332

304-332

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.

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