DUAL SPACE AND HYPERDIMENSION OF COMPACT HYPERGROUPS

We characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite hypergroups. Also, studying the representation theory of finite hypergroups, we highlight some interesting differences and similarities between the representation theories of finite hypergroups and finite groups. Finally, we compute the Heisenberg inequality for compact hypergroups.

Uncertainty Principles on Weighted Spheres, Balls, and Simplexes

This paper studies the uncertainty principle for spherical h-harmonic expansions on the unit sphere of ℝ d associated with a weight function invariant under a general finite reflection group, which is in full analogy with the classical Heisenberg inequality. Our proof is motivated by a new decomposition of the Dunkl–Laplace–Beltrami operator on the weighted sphere.

ON HEISENBERG INEQUALITY

A Heisenberg inequality, involving a differentiation operator, its adjoint, and the second quantization operator of a unitary operator, is proved in the context of white noise analysis.