Weak uncertainty principle for fractals, graphs and metric measure spaces

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 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.

Cited by in corpus (9)

• Spectral dimension and Bohr's formula for Schrodinger operators on unbounded fractal spaces
• Singularly continuous spectrum of a self-similar Laplacian on the half-line
• Isoperimetric weights and generalized uncertainty inequalities in metric measure spaces
• Fractal AC circuits and propagating waves on fractals
• BV functions and fractional Laplacians on Dirichlet spaces
• Gaps in the spectrum of the Laplacian on $3N$-Gaskets
• Families of spectral sets for Bernoulli convolutions
• Fractional uncertainty
• Uncertainty inequalities on groups and homogeneous spaces via isoperimetric inequalities