Differentiability of spectral functions for symmetric 𝛼-stable processes

Takeda, Masayoshi; Tsuchida, Kaneharu

doi:10.1090/S0002-9947-07-04149-9

Differentiability of spectral functions for symmetric $\alpha$-stable processes
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by Masayoshi Takeda and Kaneharu Tsuchida PDF

Trans. Amer. Math. Soc. 359 (2007), 4031-4054 Request permission

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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