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ISSN 1088-6850(e) ISSN 0002-9947(p)

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
MathSciNet review: 2302522
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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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