JournalsrmiVol. 31, No. 2pp. 461–476

Exponentially sparse representations of Fourier integral operators

  • Elena Cordero

    Università degli Studi di Torino, Italy
  • Fabio Nicola

    Politecnico di Torino, Italy
  • Luigi Rodino

    Università degli Studi di Torino, Italy
Exponentially sparse representations of Fourier integral operators cover
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Abstract

We investigate the sparsity of the Gabor-matrix representation of Fourier integral operators with a phase having quadratic growth. It is known that such an infinite matrix is sparse and well organized, being in fact concentrated along the graph of the corresponding canonical transformation. Here we show that, if the phase and symbol have a regularity of Gevrey type of order s>1s>1 or analytic (s=1s=1), the above decay is in fact sub-exponential or exponential, respectively. We also show by a counterexample that ultra-analytic regularity (s<1s<1) does not give super-exponential decay. This is in sharp contrast to the more favorable case of pseudodifferential operators, or even (generalized) metaplectic operators, which are treated as well.

Cite this article

Elena Cordero, Fabio Nicola, Luigi Rodino, Exponentially sparse representations of Fourier integral operators. Rev. Mat. Iberoam. 31 (2015), no. 2, pp. 461–476

DOI 10.4171/RMI/841