Differentiability of spectral functions for symmetric $\alpha$-stable processes
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Abstract:
Let $\mu$ be a signed Radon measure in the Kato class and define a Schrödinger type operator $\mathcal {H}^{\lambda \mu }=\frac {1}{2}(-\Delta )^{\frac {\alpha }{2}} + \lambda \mu$ on $\mathbb {R}^d$. We show that its spectral bound $C(\lambda )=-\inf \sigma (\mathcal {H}^{\lambda \mu })$ is differentiable if $\alpha <d\leq 2\alpha$ and $\mu$ is Green-tight.References
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Additional Information
- Masayoshi Takeda
- Affiliation: Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan
- MR Author ID: 211690
- Email: takeda@math.tohoku.ac.jp
- Kaneharu Tsuchida
- Affiliation: Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan
- Email: kanedon@ma8.seikyou.ne.jp
- Received by editor(s): February 25, 2004
- Received by editor(s) in revised form: August 16, 2005
- Published electronically: March 20, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 4031-4054
- MSC (2000): Primary 60J45, 60J40, 35J10
- DOI: https://doi.org/10.1090/S0002-9947-07-04149-9
- MathSciNet review: 2302522