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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


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.


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

Primary: 60J25
Secondary: 60J27

Keywords: Diffusion operators , First Dirichlet eigenvalue , Hardy inequality , recurrence , transience , variational formula

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