Analysis on Graphs and Fractals

Uncertainty principle for fractals, graphs and metric measure spaces

KA Okoudjou, Univeristy of Maryland, USA

Abstract

We formulate and prove weak uncertainty principles for functions defined on fractals, graphs and more generally on metric measure spaces. In particular, this uncertainty inequality is proved under different assumptions such as an appropriate measure growth condition with respect to a specific metric, or in the absence of such a metric, we assume the Poincare inequality and the reverse volume doubling property. We also consider the weak uncertainty inequality in the context of Nash-type inequalities.