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A New Proof of Global SmoothingEstimates for Dispersive Equations

  • Michael Ruzhansky
  • Mitsuru Sugimoto
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 155)

Abstract

The aim of this article is to provide a new method to prove global smoothing estimates for dispersive equations such as Schrödinger equations. For the purpose, the Egorov-type theorem via canonical transformation in the form of a class of Fourier integral operators is established, and their weighted L2-boundedness is also proved. The boundedness result is not covered by previous one such as Asada and Fujiwara [1]. By using them, a different proof for the result obtained by Ben-Artzi & Klainerman [2] is provided. This new idea gives a clear understanding of smoothing effects of dispersive equations, and further developments are also expected. In fact, some extended results based on the same idea are also announced.

Keywords

Dispersive equation smoothing effect canonical transformation 

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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Michael Ruzhansky
    • 1
  • Mitsuru Sugimoto
    • 2
  1. 1.Department of MathematicsImperial CollegeLondonUK
  2. 2.Department of Mathematics Graduate School of ScienceOsaka UniversityToyonaka OsakaJapan

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