The $L^p$-continuity of Wave Operators for One Dimensional Schrödinger Operators

J. Math. Sci. Univ. Tokyo
Vol. 7 (2000), No. 2, Page 221--240.

Artbazar, Galtbayar ; Yajima, Kenji
The $L^p$-continuity of Wave Operators for One Dimensional Schrödinger Operators
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Abstract:
We consider the wave operators $W_\pm u = {\rm s-} \lim_{t \to \pm \infty} e^{itH}e^{-itH_0}u $ for a pair of \Schr operators ${\dsize H_0= -\frac{d^2}{dx^2}}$ and $H=H_0+V(x)$ on the line $\rbf$. We show that $W_\pm$ is bounded in $L^p(\rbf)$ for any $1
Mathematics Subject Classification (1991): Primary 81U05, 34L25; Secondary 42B20, 34L40
Mathematical Reviews Number: MR1768465

Received: 1999-05-10