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2009 First Eigenvalue of One-dimensional Diffusion Processes
Jian Wang
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Electron. Commun. Probab. 14: 232-244 (2009). DOI: 10.1214/ECP.v14-1464

Abstract

We consider the first Dirichlet eigenvalue of diffusion operators on the half line. A criterion for the equivalence of the first Dirichlet eigenvalue with respect to the maximum domain and that to the minimum domain is presented. We also describle the relationships between the first Dirichlet eigenvalue of transient diffusion operators and the standard Muckenhoupt's conditions for the dual weighted Hardy inequality. Pinsky's result [17] and Chen's variational formulas [8] are reviewed, and both provide the original motivation for this research.

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Jian Wang. "First Eigenvalue of One-dimensional Diffusion Processes." Electron. Commun. Probab. 14 232 - 244, 2009. https://doi.org/10.1214/ECP.v14-1464

Information

Accepted: 24 May 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1192.60090
MathSciNet: MR2507752
Digital Object Identifier: 10.1214/ECP.v14-1464

Subjects:
Primary: 60J25
Secondary: 60J27

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