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.References
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Additional Information
- Kasso A. Okoudjou
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015
- MR Author ID: 721460
- ORCID: setImmediate$0.18192135121667974$6
- Email: kasso@math.umd.edu
- Laurent Saloff-Coste
- Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201
- MR Author ID: 153585
- Email: lsc@math.cornell.edu
- Alexander Teplyaev
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269-3009
- MR Author ID: 361814
- Email: teplyaev@math.uconn.edu
- Received by editor(s): August 15, 2006
- Published electronically: February 27, 2008
- Additional Notes: The second author was supported in part by NSF grant DMS-0603886
The third author was supported in part by NSF grant DMS-0505622 - © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 3857-3873
- MSC (2000): Primary 28A80, 42C99; Secondary 26D99
- DOI: https://doi.org/10.1090/S0002-9947-08-04472-3
- MathSciNet review: 2386249