Wave Operators for Schrödinger Operators with Threshold Singuralities, Revisited

2015/08/24 by Yajima, Kenji
#81U05 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1508.05738

Abstract

The continuity property in the Sobolev space W^k,p(\bf R^m) of wave operators of scattering theory for m-dimensional single-body Schrödinger operator is considered when the resolvent of the operator has singularities at the bottom of the continuous spectrum. It is shown that they are continuous in W^k,p(\bf R^m), 0≤ k ≤ 2, for 13 if m=3 and, for 1m/2 if m≥ 5. This extends the previously known interval of p for the continuity, 3/2

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