Communications in Mathematical Physics

, Volume 216, Issue 1, pp 195–213

First KdV Integrals¶and Absolutely Continuous Spectrum¶for 1-D Schrödinger Operator

  • S. Molchanov
  • M. Novitskii
  • B. Vainberg

DOI: 10.1007/s002200000333

Cite this article as:
Molchanov, S., Novitskii, M. & Vainberg, B. Commun. Math. Phys. (2001) 216: 195. doi:10.1007/s002200000333

Abstract:

We consider 1-D Schrödinger operators on L2(R+) with slowly decaying potentials. Under some conditions on the potential, related to the first integrals of the KdV equation, we prove that the a.c. spectrum of the operator coincides with the positive semiaxis and the singular spectrum is unstable. Examples show that for special classes of sparse potentials these results can not be improved.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • S. Molchanov
    • 1
  • M. Novitskii
    • 2
  • B. Vainberg
    • 1
  1. 1.Mathematics, UNCC, Charlotte, NC 28223, USA.¶E-mail: smolchan@uncc.edu; brvainbe@uncc.eduUS
  2. 2.Mathematics, ILT, Kharkov, 310164, Ukraine.¶E-mail: novitskii@ilt.kharkov.uaUA