GARETTO, C., 2008. Generalized Fourier integral operators on spaces of Colombeau type.IN: Rodino, L. and Wong, M.W. (eds). New Developments in Pseudo-Differential Operators. Basel: Birkhauser-Verlag, pp. 137-184.
Operator Theory: Advances and Operations;189
Generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is based on a theory of generalized oscillatory integrals (OIs) whose phase functions as well as amplitudes may be generalized functions of Colombeau type. The mapping properties of these FIOs are studied as the composition with a generalized pseudodifferential operator. Finally, the microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wave front sets are investigated. This theory of generalized FIOs is motivated by the need of a general framework for partial differential operators with non-smooth coefficients and distributional data.
This book chapter is closed access.
This work was completed with the support of FWF (Austria), grants T305-N13 and Y237-N13.