Heisenberg uncertainty principle on Chébli–Trimèche hypergroups

Ruiqin Ma

Vol. 235 (2008), No. 2, 289–296

DOI: 10.2140/pjm.2008.235.289

Abstract

An uncertainty principle on Chébli–Trimèche hypergroups is established, as a generalization of Heisenberg inequalities for Jacobi transforms proved in my previous paper. It implies and extends the uncertainty principle for Hankel transforms by M. Rösler and M. Voit. The proof is based on ultracontractive properties of the semigroups generated by a second order differential operator and on the estimate of the heat kernel.

Keywords

uncertainty principle, hypergroups

Mathematical Subject Classification 2000

Primary: 43A62

Secondary: 44A15

Milestones

Received: 20 August 2007

Revised: 5 December 2007

Accepted: 23 January 2008

Published: 1 April 2008