Electronic Communications in Probability

First Eigenvalue of One-dimensional Diffusion Processes

Jian Wang

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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.

Article information

Electron. Commun. Probab., Volume 14 (2009), paper no. 23, 232-244.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces

First Dirichlet eigenvalue Hardy inequality variational formula transience recurrence diffusion operators

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Wang, Jian. First Eigenvalue of One-dimensional Diffusion Processes. Electron. Commun. Probab. 14 (2009), paper no. 23, 232--244. doi:10.1214/ECP.v14-1464. https://projecteuclid.org/euclid.ecp/1465234732

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