Generalized uncertainty inequalities

Abstract

In this paper, Heisenberg-Pauli-Weyl-type uncertainty inequalities are obtained for a pair of positive-self adjoint operators on a Hilbert space, whose spectral projectors satisfy a ``balance condition'' involving certain operator norms. This result is then applied to obtain uncertainty inequalities on Riemannian manifolds, Riemannian symmetric spaces of non-compact type, homogeneous graphs and unimodular Lie groups with sublaplacians.

19 pages

Cited by in corpus (4)

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• Isoperimetric weights and generalized uncertainty inequalities in metric measure spaces
• Weighted inequalities and uncertainty principles for the $(\mathbf{k},\mathbf{a})$-generalized Fourier transform
• Uncertainty inequalities on groups and homogeneous spaces via isoperimetric inequalities