Weak uncertainty principle for fractals, graphs and metric measure spaces

Details Weak uncertainty principle for fractals, graphs and metric measure spaces Weak uncertainty principle for fractals, graphs and metric measure spaces

2007-01-07

arxiv.org/abs/math/0701207v1

Mathematics

Functional Analysis

Scientific paper

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 Poincare 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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