Minimizing functions for an uncertainty principle on locally compact groups of bounded representation dimension

Eberhard Kaniuth
2006 Proceedings of the American Mathematical Society  
Let G be a locally compact group of bounded representation dimension d(G). Then, for any integrable function f on G, the product of the measures of the support of f and the support of its operator-valued Fourier transform on the dual space of G is bounded below by 1/d(G). We classify all functions for which equality holds and prove criteria for when such functions exist.
doi:10.1090/s0002-9939-06-08451-6 fatcat:c5i26qouu5hznjngy7rkfzod4a