GARETTO, C., OBERGUGGENBERGER, M. and HÖRMANN, G., 2009. Generalized oscillatory integrals and Fourier integral operators. Proceedings of the Edinburgh Mathematical Society, 52 (2), pp. 351-386.
In this paper, a theory is developed of generalized oscillatory integrals (OIs) whose phase functions and amplitudes may be generalized functions of Colombeau type. Based on this, generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is motivated by the need for a general framework for partial differential operators with non-smooth coefficients and distribution dataffi The mapping properties of these FIOs are studied, as is microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wavefront sets.
C.G. was supported by FWF (Austria) Grant no. P16820-
N04 and TWF (Tyrol) Grant no. UNI-0404/305. G.H. was supported by FWF (Austria)
Grant no. P16820-N04. M.O. was partly supported by FWF (Austria) Grant no. Y237.