Generalized uncertainty inequalities

The Heisenberg-Pauli-Weyl (HPW) uncertainty inequality on ℝn says that,. Let H be a Hilbert space; we obtain inequalities of the form,. for a pair of positive self-adjoint operators T, L on H satisfying a "balance condition" involving certain operator norms of their spectral projectors. This extends a result of Ciatti et al. (Adv Math 215(2):616-625, 2007) since our hypotheses allow growth rates other than polynomial, e.g., exponential ones. As examples of applications, we obtain HPW-type inequalities on Riemannian manifolds, Riemannian symmetric spaces of non-compact type, homogeneous graphs and unimodular Lie groups. © 2009 Springer-Verlag.