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Perturbations of One-Dimensional Schrödinger Operators Preserving the Absolutely Continuous Spectrum


Killip, Rowan Brett (2001) Perturbations of One-Dimensional Schrödinger Operators Preserving the Absolutely Continuous Spectrum. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2t54-0b07.


NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. We study the stability of the absolutely continuous spectrum of one-dimensional Schrodinger operators [...] with periodic potentials q(x). Specifically, it is proved that any perturbation of the potential, [...], preserves the essential support (and multiplicity) of the absolutely continuous spectrum. This is optimal in terms of [...] spaces and, for [...], it answers in the affirmative a conjecture of Kiselev, Last and Simon. By adding constraints on the Fourier transform of V, it is possible to relax the decay assumptions on V. It is proved that if [...] and [...] is uniformly locally square integrable, then preservation of the a.c. spectrum still holds. If we assume that [...], still stronger results follow: if [...] and [...] is square integrable on an interval [...], then the interval [...] is contained in the essential support of the absolutely continuous spectrum of the perturbed operator.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mathematics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Simon, Barry M.
Thesis Committee:
  • Simon, Barry M. (chair)
  • Hundertmark, Dirk
  • Kiselev, S.
  • Last, Y.
Defense Date:8 August 2000
Record Number:CaltechETD:etd-09062005-102553
Persistent URL:
Killip, Rowan Brett0000-0002-4272-7916
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3350
Deposited By: Imported from ETD-db
Deposited On:06 Sep 2005
Last Modified:12 Sep 2022 22:33

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