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asymptotic expansion bicharacteristic strips Boutet de Monvel characteristic set choose codimension compact set cone supp conic neighborhood defined Definition denote differential operator distribution f distribution kernel Duistermaat elliptic Fourier integral elliptic operator exists a proper ferential operator following result Fourier integral operators Fourier transform ft x ft ft x IRn functions on ft Hamiltonian fields hence homogeneous of degree Hormander hypoelliptic hypoelliptic operators integral curves lemma Let f loc loc micro-functions modulo Monvel multi-indices neighborhood never vanishes Om(U open set operator of degree operator with simple oscillating integral parametrix partial differential phase function Poisson bracket Proof proper pseudo-differential operator pseudo quotient space resp set in IRn sheaf simple characteristics Sing Sp f sing supp f singular spectrum singular support Sjostrand Sm(ft smooth solutions space symbol of degree T*fi T*ft theorem tion topology total symbol well-posed problem