Wiener algebras of Fourier integral operators

By Elena Cordero, Karlheinz Gröchenig, Fabio Di Nicola, L. Rodino. 2013

83 citations recorded by the source corpus.

Abstract We construct a one-parameter family of algebras FIO ( Ξ , s ) , 0 ⩽ s ⩽ ∞ , consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of the operators in FIO ( Ξ , s ) . 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 = ∞ , 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eeab67ccef65e2ca9a8906986ec21e3f415b1be3