Weak uncertainty principle for fractals, graphs and metric measure spaces

2007/01/07 by Kasso A. Okoudjou, Kasso Okoudjou, Laurent Saloff‐Coste +2 · 2 citations
Computer Science · Mathematics · #Computer science #Context (archaeology) #Discrete mathematics #Fractal #Inequality #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Measure (data warehouse) #Metric (unit) #Metric space #Pure mathematics #Topological and Geometric Data Analysis #math.FA #math.MG #msc:26D99 #msc:28A80 #msc:42C99

paper · pdf · doi:10.1090/s0002-9947-08-04472-3

published as Trans. Amer. Math. Soc. 360 (2008), no. 7, 3857-3873

arxiv created 2007/01/07 · openalex publication_date 2008/02/27 · arxiv updated 2018/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Fractals in the Large
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• The uncertainty principle: A mathematical survey

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