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.

Generalized Hilbert bialgebras of compact type and their representations

Yu. A. Chapovsky, A. A. Kalyuzhnyi

MFAT 11 (2005), no. 3, 222-233

222-233

On the inverse spectral problem for a commutative field of operator-valued Jacobi matrices

Yu. A. Chapovsky

MFAT 8 (2002), no. 1, 14-22

14-22

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