Scattering length for stable processes

Abstract

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 Schrödinger operator of the ``Neumann'' fractional Laplacian in a cube with potential $v$.

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