Papers

Peer-reviewed
Dec, 2009

SINGULARITIES OF SOLUTIONS TO THE SCHRODINGER EQUATION ON SCATTERING MANIFOLD

AMERICAN JOURNAL OF MATHEMATICS
  • Kenichi Ito
  • ,
  • Shu Nakamura

Volume
131
Number
6
First page
1835
Last page
1865
Language
English
Publishing type
Research paper (scientific journal)
DOI
10.1353/ajm.0.0087
Publisher
JOHNS HOPKINS UNIV PRESS

In this paper we study microlocal singularities of solutions to Schrodinger equations on scattering manifolds, i.e.. noncompact Riemannian manifolds with asymptotically conic ends. We characterize the wave front set of the solutions in terms of the initial condition and the classical scattering maps under the nontrapping condition. Our result is closely related to a recent work by Hassell and Wunsch, though our model is more general and the method, which relies heavily on scattering theoretical ideas, is simple and quite different. In particular, we use an Egorov-type argument in the standard pseudodifferential symbol classes, and avoid using Legendre distributions. In the proof, we employ a microlocal smoothing property in terms of the radially homogenous wave front set, which is more precise than the preceding results.

Link information
DOI
https://doi.org/10.1353/ajm.0.0087
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000272641900010&DestApp=WOS_CPL
ID information
  • DOI : 10.1353/ajm.0.0087
  • ISSN : 0002-9327
  • Web of Science ID : WOS:000272641900010

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