$\alpha$-continuity properties of the symmetric $\alpha$-stable process
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- by R. Dante DeBlassie and Pedro J. Méndez-Hernández PDF
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Abstract:
Let $D$ be a domain of finite Lebesgue measure in $\mathbb {R}^d$ and let $X^D_t$ be the symmetric $\alpha$-stable process killed upon exiting $D$. Each element of the set $\{ \lambda _i^\alpha \}_{i=1}^\infty$ of eigenvalues associated to $X^D_t$, regarded as a function of $\alpha \in (0,2)$, is right continuous. In addition, if $D$ is Lipschitz and bounded, then each $\lambda _i^\alpha$ is continuous in $\alpha$ and the set of associated eigenfunctions is precompact.References
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Additional Information
- R. Dante DeBlassie
- Affiliation: Department of Mathematics, Texas A & M University, College Station, Texas 77843
- Email: deblass@math.tamu.edu
- Pedro J. Méndez-Hernández
- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
- Address at time of publication: Escuela de Matemática, Universidad de Costa Rica, San Pedro de Montes de Oca, Costa Rica
- Email: mendez@math.utah.edu
- Received by editor(s): July 9, 2004
- Received by editor(s) in revised form: April 4, 2005
- Published electronically: December 19, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 2343-2359
- MSC (2000): Primary 60J45
- DOI: https://doi.org/10.1090/S0002-9947-06-04032-3
- MathSciNet review: 2276623