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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