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Dedicated to Mikhail Shubin on the occasion of his sixty-fifth birthday Abstract. We consider the scattering transform for the Schrodinger equation with a singular potential and no bound states. Using the Riccati representation for real-valued potentials on the line, we obtain invertibility and Lipschitz con- tinuity of the scattering transform between weighted and Sobolev spaces. Our approach exploits the connection between scattering theory for the Schrodinger equation and scattering theory for the ZS-AKNS system.

Sobolev mapping properties of the scattering transform for the Schrödinger equation