Scattering length for stable processes

Details Scattering length for stable processes Scattering length for stable processes

2006-03-27

arxiv.org/abs/math/0603627v2

Mathematics

Probability

preprint

Scientific paper

Let $\alpha\in(0,2)$ and $X_t$ be a symmetric $\alpha$-stable process. We
define the scattering length $\Gamma(v)$ of the positive potential $v$ and
prove several of its basic properties. We use the scattering length to
findestimates for the first eigenvalue of the Schr\"odinger operator of the
``Neumann'' fractional Laplacian in a cube with potential $v$.

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