Illinois Journal of Mathematics

Scattering length for stable processes

Bartłomiej Siudeja

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Let $0<\alpha<2$ and $X_t$ be the isotropic $\alpha$-stable Lévy process. We define scattering length $\Gamma(v)$ of a positive potential $v$. We use the scattering length to find estimates for the first eigenvalue of the Schrödinger operator of the “Neumann” fractional Laplacian in a cube with a potential $v$.

Article information

Illinois J. Math., Volume 52, Number 2 (2008), 667-680.

First available in Project Euclid: 23 July 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G52: Stable processes
Secondary: 31C15: Potentials and capacities


Siudeja, Bartłomiej. Scattering length for stable processes. Illinois J. Math. 52 (2008), no. 2, 667--680. doi:10.1215/ijm/1248355357.

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