Transactions of the American Mathematical Society

Differentiability of spectral functions for symmetric $\alpha$ -stable processes

Author(s): Masayoshi Takeda; Kaneharu Tsuchida
Journal: Trans. Amer. Math. Soc. 359 (2007), 4031-4054.
MSC (2000): Primary 60J45, 60J40, 35J10
Posted: March 20, 2007
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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.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 60J45, 60J40, 35J10

Masayoshi Takeda
Affiliation: Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan
Email: takeda@math.tohoku.ac.jp

Kaneharu Tsuchida
Affiliation: Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan
Email: kanedon@ma8.seikyou.ne.jp

DOI: 10.1090/S0002-9947-07-04149-9
PII: S 0002-9947(07)04149-9
Keywords: Symmetric stable process, spectral function, criticality, additive functional, Kato measure
Received by editor(s): February 25, 2004
Received by editor(s) in revised form: August 16, 2005
Posted: March 20, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

Masayoshi Takeda; Kaneharu Tsuchida , Differentiability of spectral functions for symmetric $\alpha$-stable processes, Trans. Amer. Math. Soc. 359 (2007), 4031-4054.

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