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

2007/10/23 by Vidian Rousse, Rousse, Vidian, Torben Swart +1
Mathematics · #35S30 #46F12 #81Q20 #81S30 #Advanced Harmonic Analysis Research #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.0710.4200

openalex publication_date 2007/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^*\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 L² into itself are proven.

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