Communications in Mathematical Physics

, Volume 203, Issue 2, pp 341–347 | Cite as

On the Absolutely Continuous Spectrum¶of One-Dimensional Schrödinger Operators¶with Square Summable Potentials

  • P. Deift
  • R. Killip


For continuous and discrete one-dimensional Schrödinger operators with square summable potentials, the absolutely continuous part of the spectrum is essentially supported by [0,∞) and [−2,2] respectively. This fact is proved by considering a priori estimates for the transmission coefficient.


Continuous Spectrum Transmission Coefficient Continuous Part Summable Potential 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • P. Deift
    • 1
  • R. Killip
    • 2
  1. 1.Courant Institute, 251 Mercer St., New York, NY 10012, USA. E-mail: deift@cims.nyu.eduUS
  2. 2.Mathematics 253-37, Caltech, Pasadena, CA 91125, USA. E-mail: killip@cco.caltech.eduUS

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