α-Continuity Properties of Stable Processes
| dc.creator | DeBlassie, R. D. | |
| dc.creator | Mendez-Hernandez, Pedro J. | |
| dc.date | 2004-07-19 | |
| dc.date.accessioned | 2026-07-07T05:10:27Z | |
| dc.date.available | 2026-07-07T05:10:27Z | |
| dc.description | Let $D$ be a domain of finite Lebesgue measure in $\bR^d$ and let $X^D_t$ be the symmetric $α$-stable process killed upon exiting $D$. Each element of the set $\{λ_i^α\}_{i=1}^\infty$ of eigenvalues associated to $X^D_t$, regarded as a function of $α\in(0,2)$, is right continuous. In addition, if $D$ is Lipschitz and bounded, then each $ λ_i^α$ is continuous in $α$ and the set of associated eigenfunctions is precompact. We also prove that if $D$ is a domain of finite Lebesgue measure, then for all $0<α<β\leq 2$ and $i\geq 1$, \[λ_i^α\leq [ λ^β_i]^{α/β}.\] Previously, this bound had been known only for $β=2$ and $α$ rational. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0407318 | |
| dc.identifier | http://arxiv.org/abs/math/0407318 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71935 | |
| dc.subject | Probability | |
| dc.subject | Spectral Theory | |
| dc.subject | 60J45, 26A33 | |
| dc.title | α-Continuity Properties of Stable Processes | |
| dc.type | text |