Journal of Fourier Analysis and Applications

, Volume 18, Issue 4, pp 661–684 | Cite as

Approximation of Fourier Integral Operators by Gabor Multipliers

  • Elena Cordero
  • Karlheinz GröchenigEmail author
  • Fabio Nicola


A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this principle for Fourier integral operators with a smooth phase and a symbol in the Sjöstrand class and use Gabor frames as wave packets. The almost diagonalization of such Fourier integral operators suggests a specific approximation by (a sum of) elementary operators, namely modified Gabor multipliers. We derive error estimates for such approximations. The methods are taken from time-frequency analysis.


Fourier integral operators Modulation spaces Short-time Fourier transform Gabor multipliers 

Mathematics Subject Classification (2000)

35S30 47G30 42C15 



The authors would like to thank the anonymous referees for their valuable comments. K.G. was supported in part by the project P22746-N13 of the Austrian Science Foundation (FWF).


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Elena Cordero
    • 1
  • Karlheinz Gröchenig
    • 2
    Email author
  • Fabio Nicola
    • 3
  1. 1.Department of MathematicsUniversity of TorinoTorinoItaly
  2. 2.Faculty of MathematicsUniversity of ViennaViennaAustria
  3. 3.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly

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