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First Eigenvalue of One-dimensional Diffusion Processes
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Jian Wang, School of Mathematics and Computer Science, Fujian Normal University
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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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Full text: PDF
Pages: 232-244
Published on: May 24, 2009
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Electronic Communications in Probability. ISSN: 1083-589X |
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