Communications in Mathematical Physics

, Volume 208, Issue 1, pp 125–152

Lp-Boundedness of Wave Operators for¶Two Dimensional Schrödinger Operators

  • Kenji Yajima
Original article

DOI: 10.1007/s002200050751

Cite this article as:
Yajima, K. Comm Math Phys (1999) 208: 125. doi:10.1007/s002200050751

Abstract:

Let \(\) be the two dimensional Schrödinger operator with the real valued potential V which satisfies the decay condition at infinity \(\) for \(\). We show that the wave operators \(\), \(\), are bounded in \(\) for any 1<p<∞ under the condition that H has no zero bound states or zero resonance, extending the corresponding results for higher dimensions. As W± intertwine H0 and the absolutely continuous part H Pac of H : f(H)Pac=W±f(H0 )W±* for any Borel function f on ℝ1, this reduces the various Lp-mapping properties of f(H)Pac to those of f(H)0), the convolution operator by the Fourier transform of the function f2).

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Kenji Yajima
    • 1
  1. 1.Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153 JapanJP