Schatten class Fourier integral operators

作者：Bishop Shannon^*

来源：Applied and Computational Harmonic Analysis, 2011, 31(2): 205-217.

DOI：10.1016/j.acha.2010.11.001

• Fourier integral operators
• Schatten class operators
• Gabor frames
• Gabor transform
• Modulation spaces

Fourier integral operators with sufficiently smooth phase act on the time-frequency content. of functions: However time-frequency analysis has only recently been used to analyze these operators. In this paper, we show that if a Fourier integral operator has a smooth phase function and its symbol is well localized in time and frequency, then the operator is Schatten p-class for p is an element of [1, 2], with inclusion of the symbol in mixed modulation spaces serving as the appropriate measure of time-frequency localization. Our main results are sharp in the sense that larger mixed modulation spaces necessarily contain symbols of Fourier integral operators that are not Schatten p-class. Published by Elsevier Inc.

• 出版日期2011-9