00-352 Jonathan Butler

Global $ h $ Fourier integral operators with complex-valued phase functions (42K, AMS-TeX) Sep 9, 00

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Abstract. We consider globally defined $ h $ Fourier integral operators ($ h $ F.I.O.) with complex-valued phase functions. Symbolic calculus of $ h $ F.I.O. is considered and, using a new complex Gauss transform, composition of $ h $ pseudodifferential operators ($ h $ P.D.O.) and $ h $ F.I.O. is considered. For a self-adjoint $ h $ P.D.O. $ A(h) $ and $ h $ P.D.O. $ P(h) $ and $ Q(h) $ with compactly supported symbols, we apply the results to approximate the kernel of the operator $$ U_{P,Q}(t;h) := P(h) e^{-ih^{-1}tA(h)} Q(h)^*, t \in \Bbb R , h > 0 , $$ by a single, globally defined $ h $ oscillatory integral.

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