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Dispersive properties of Schrodinger equations

Citation

Cai, Kaihua (2005) Dispersive properties of Schrodinger equations. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-06022005-153453

Abstract

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) caltech.edu
Record Number:CaltechETD:etd-06022005-153453
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-06022005-153453
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2392
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:03 Jun 2005
Last Modified:26 Dec 2012 02:50

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