We construct a one-parameter family of algebras consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of the operators in this algebra. The operator algebra is defined by the decay properties of an associated Gabor matrix around the graph of the canonical transformation. In particular, for the limit case s=\infty, our Gabor technique provides a new approach to the analysis of S_{0,0}^0-type Fourier integral operators, for which the global calculus represents a still open relevant problem.

Wiener Algebras of Fourier Integral Operators

CORDERO, Elena;RODINO, Luigi Giacomo
2013-01-01

Abstract

We construct a one-parameter family of algebras consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of the operators in this algebra. The operator algebra is defined by the decay properties of an associated Gabor matrix around the graph of the canonical transformation. In particular, for the limit case s=\infty, our Gabor technique provides a new approach to the analysis of S_{0,0}^0-type Fourier integral operators, for which the global calculus represents a still open relevant problem.
2013
99
219
233
http://arxiv.org/pdf/1011.0648.pdf
http://dx.doi.org/10.1016/j.matpur.2012.06.012
Fourier Integral operators; modulation spaces; short-time Fourier transform; Gabor frames; Wiener algebra
Elena Cordero; Karlheinz Gröchenig; Fabio Nicola; Luigi Rodino
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/130438
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