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A Remark on Lp-Boundedness of Wave Operators¶for Two Dimensional Schrödinger Operators

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Abstract:

Let H=−Δ+V be a two dimensional Schrödinger operator with a real potential V(x) satisfying the decay condition , δ > 6. Let H 0=−Δ. We show that the wave operators are bounded in L p(R 2) under the condition that H has no zero resonances or bound states. In this paper the condition , imposed in a previous paper (K. Yajima, Commun. Math. Phys. 208, 125–152 (1999)), is removed.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan. E-mail: yajima@ms.u-tokyo.ac.jp, , , , , , JP

    Arne Jensen & Kenji Yajima

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  1. Arne Jensen
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  2. Kenji Yajima
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Received: 13 September 2001 / Accepted: 15 October 2001

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Jensen, A., Yajima, K. A Remark on Lp-Boundedness of Wave Operators¶for Two Dimensional Schrödinger Operators. Commun. Math. Phys. 225, 633–637 (2002). https://doi.org/10.1007/s002200100603

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  • DOI: https://doi.org/10.1007/s002200100603

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