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

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

2007-10-23

arxiv.org/abs/0710.4200v3

Physics

Mathematical Physics

29 pages

Scientific paper

In this work, a class of semiclassical Fourier Integral Operators (FIOs) with
complex phase associated to some canonical transformation of the phase space
$T^*\R^d$ 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.

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