Time-Frequency Analysis of Fourier Integral Operators
Analysis of PDEs
2016-06-28 v1 Numerical Analysis
Abstract
We use time-frequency methods for the study of Fourier Integral operators (FIOs). In this paper we shall show that Gabor frames provide very efficient representations for a large class of FIOs. Indeed, similarly to the case of shearlets and curvelets frames, the matrix representation of a Fourier Integral Operator with respect to a Gabor frame is well-organized. This is used as a powerful tool to study the boundedness of FIOs on modulation spaces. As special cases, we recapture boundedness results on modulation spaces for pseudo-differential operators with symbols in , for some unimodular Fourier multipliers and metaplectic operators.
Cite
@article{arxiv.0710.3652,
title = {Time-Frequency Analysis of Fourier Integral Operators},
author = {Elena Cordero and Fabio Nicola and Luigi Rodino},
journal= {arXiv preprint arXiv:0710.3652},
year = {2016}
}