Wiener Algebras of Fourier Integral Operators

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.