Abstract
Let H 0 be a radially symmetric function of the momentum − i∇ in \( {L^2}({\mathbb{R}^n}) \) and let H be a selfadjoint operator bounded from below. It is given a criterion for the asymptotic completeness of the scattering system {H 0, H} in terms of the semigroup difference \( {e^{ - sH}} - {e^{ - s{H_0}}}, \), where s > 0 is an arbitrary fixed value. The result is applied to H 0 = (− Δ)α/2.
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The first author would like to dedicate this article to Jean Michel Combes on the occasion of his sixtieth birthday
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Demuth, M., Giere, E., Sinha, K.B. (2001). A Semigroup Criterion for the Completeness of Scattering Systems. In: Demuth, M., Schulze, BW. (eds) Partial Differential Equations and Spectral Theory. Operator Theory: Advances and Applications, vol 126. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8231-6_11
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DOI: https://doi.org/10.1007/978-3-0348-8231-6_11
Publisher Name: Birkhäuser, Basel
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