Weak uncertainty principle for fractals, graphs and metric measure spaces

Okoudjou, Kasso; Saloff-Coste, Laurent; Teplyaev, Alexander

doi:10.1090/S0002-9947-08-04472-3

Weak uncertainty principle for fractals, graphs and metric measure spaces
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by Kasso A. Okoudjou, Laurent Saloff-Coste and Alexander Teplyaev PDF

Trans. Amer. Math. Soc. 360 (2008), 3857-3873 Request permission

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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