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On the Mapping Properties of the Wave Operators in Scattering Theory

In: Mathematical Physics X

Author

Listed:
  • Arne Jensen

    (Aalborg University, Department of Mathematics and Computer Science, Institute for Electronic Systems)

  • Shu Nakamura

    (University of Tokyo, Department of Pure and Applied Sciences)

Abstract

In this note we describe some recent results on the mapping properties of the wave operators for two-body Schrödinger operators with long range potentials. We show that the wave operators and adjoint wave operators, localized in energy, map a weighted L 2-space into a slightly larger weighted L 2 -space. We also give some preliminary results on the mapping properties between the L p -spaces. The precise statement of the results requires some preparation.

Suggested Citation

  • Arne Jensen & Shu Nakamura, 1992. "On the Mapping Properties of the Wave Operators in Scattering Theory," Springer Books, in: Konrad Schmüdgen (ed.), Mathematical Physics X, pages 447-450, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-77303-7_50
    DOI: 10.1007/978-3-642-77303-7_50
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