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.
Generalized uncertainty inequalities / Martini, A.. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 265:4(2010), pp. 831-848. [10.1007/s00209-009-0544-5]
Generalized uncertainty inequalities
Martini A.
2010
Abstract
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.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2949492