Global Calculus of Fourier Integral Operators, Weighted Estimates, and Applications to Global Analysis of Hyperbolic Equations

  • Michael Ruzhansky
  • Mitsuru Sugimoto
Part of the Operator Theory: Advances and Applications book series (OT, volume 164)

Abstract

The aim of this paper is to present certain global regularity properties of hyperbolic equations. In particular, it will be determined in what way the global decay of Cauchy data implies the global decay of solutions. For this purpose, global weighted estimates in Sobolev spaces for Fourier integral operators will be reviewed. We will also present elements of the global calculus under minimal decay assumptions on phases and amplitudes.

Keywords

Fourier integral operators hyperbolic equations global estimates 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

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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