, Volume 208, Issue 2, pp 507-520

The W k, p -Continuity of the Schrödinger Wave Operators on the Line

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Abstract:

We prove that the wave operators for the Schrödinger equation on the line are continuous on the Sobolev spaces W k, p , 1 < p < ∞. Moreover, if the potential is exceptional and , where f 1(x, 0) is a Jost solution at zero energy, the wave operators are continuous on W k ,1 and on W k ,∞.

Received: 21 April 1999 / Accepted: 15 July 1999