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Oscillatory integral operators related to pointwise convergence of Schrödinger operators

Citation

Kolasa, Lawrence A. (1994) Oscillatory integral operators related to pointwise convergence of Schrödinger operators. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:05082013-093110717

Abstract

In this thesis we consider smooth analogues of operators studied in connection with the pointwise convergence of the solution, u(x,t), (x,t) ∈ ℝ^n x ℝ, of the free Schrodinger equation to the given initial data. Such operators are interesting examples of oscillatory integral operators with degenerate phase functions, and we develop strategies to capture the oscillations and obtain sharp L^2 → L^2 bounds. We then consider, for fixed smooth t(x), the restriction of u to the surface (x,t(x)). We find that u(x,t(x)) ∈ L^2(D^n) when the initial data is in a suitable L^2-Sobolev space H^8 (ℝ^n), where s depends on conditions on t.

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:Restricted to Caltech community only
Research Advisor(s):
  • Wolff, Thomas H.
Thesis Committee:
  • Unknown, Unknown
Defense Date:25 May 1994
Record Number:CaltechTHESIS:05082013-093110717
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:05082013-093110717
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7673
Collection:CaltechTHESIS
Deposited By: Benjamin Perez
Deposited On:08 May 2013 16:49
Last Modified:08 May 2013 16:49

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