Weak uncertainty principle for fractals, graphs and metric measure spaces |
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Authors: | Kasso A. Okoudjou Laurent Saloff-Coste Alexander Teplyaev |
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Affiliation: | Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015 ; Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201 ; Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269-3009 |
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Abstract: | We develop a new approach to formulate and prove the weak uncertainty inequality, which was recently introduced by Okoudjou and Strichartz. We assume either an appropriate measure growth condition with respect to the effective resistance metric, or, in the absence of such a metric, we assume the Poincaré inequality and reverse volume doubling property. We also consider the weak uncertainty inequality in the context of Nash-type inequalities. Our results can be applied to a wide variety of metric measure spaces, including graphs, fractals and manifolds. |
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Keywords: | Uncertainty principle p.c.f. fractal Heisenberg's inequality measure metric spaces Poincar{'e} inequality self-similar graphs Sierpi{'n}ski gasket uniform finitely ramified graphs |
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