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Communications in Mathematical Physics

, Volume 225, Issue 3, pp 633–637 | Cite as

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

  • Arne Jensen
  • Kenji Yajima

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.

Keywords

Potential Versus Wave Operator Decay Condition Zero Resonance Real Potential Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Arne Jensen
    • 1
  • Kenji Yajima
    • 1
  1. 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.jpJP

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