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Dispersive properties of Schrodinger equations


Cai, Kaihua (2005) Dispersive properties of Schrodinger equations. Dissertation (Ph.D.), California Institute of Technology.


This thesis mainly concerns the dispersive properties of Schrodinger equations with certain potentials, and some of their consequences.

First, we consider the charge transfer models in R^n with n > 2. In this case, the potential is a sum of several individual real-valued potentials, each moving with constant velocities. We get an L^1 to L^infty estimate for the evolution and the asymptotic completeness of the evoution in any Sobolev space.

Second, we derive the L^1 to L^infty estimate for the Schrodinger operators with a Lame potential. The Lame potential is spatially periodic and its spectrum has the structure of finite bands. We obtain a dispersive estimate with a decay rate t^{-1/3}.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Dispersive; Schrodinger
Degree Grantor:California Institute of Technology
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Thesis Committee:
  • Schlag, Wilhelm (chair)
  • Pramanik, Malabika
  • Goldberg, Michael
  • Killip, Rowan
Defense Date:19 May 2005
Author Email:kaihua (AT)
Record Number:CaltechETD:etd-06022005-153453
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2392
Deposited By: Imported from ETD-db
Deposited On:03 Jun 2005
Last Modified:26 Dec 2012 02:50

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