Global L2-Boundedness Theorems for Semiclassical Fourier Integral Operators with Complex Phase

Abstract

In this work, a class of semiclassical Fourier Integral Operators (FIOs) with complex phase associated to some canonical transformation of the phase space $T^{\ast }{\mathbb{R}}^d$ is constructed. Upon some general boundedness assumptions on the symbol and the canonical transformation, their continuity (as operators) from the Schwartz class into itself and from $L^2$ into itself are proven.

29 pages

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