G. B. Podkolzin
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On Fourier algebra of a hypergroup constructed from a conditional expectation on a locally compact group
Methods Funct. Anal. Topology 23 (2017), no. 1, 37-50
We prove that the Fourier space of a hypergroup constructed from a conditional expectation on a locally compact group has a Banach algebra structure.
Methods Funct. Anal. Topology 21 (2015), no. 3, 246-255
We give sufficient conditions for the Fourier and the Fourier-Stieltjes spaces of a locally compact hypergroup to be Banach algebras.
Methods Funct. Anal. Topology 17 (2011), no. 4, 319-329
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.
Methods Funct. Anal. Topology 16 (2010), no. 4, 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.