Compactness of Fourier Integral Operators on weighted modulation spaces
Carmen Fern\'andez, Antonio Galbis, Eva Primo
TL;DR
This paper investigates the compactness properties of Fourier integral operators on weighted modulation spaces using Gabor frame representations, leading to improved results for pseudodifferential operators.
Contribution
It introduces a new approach to analyze compactness of Fourier integral operators on weighted modulation spaces via matrix representations.
Findings
Established criteria for compactness of Fourier integral operators
Improved existing results for pseudodifferential operators
Provided a new framework using Gabor frames for operator analysis
Abstract
Using the matrix representation of Fourier integral operators with respect to a Gabor frame, we study their compactness on weighted modulation spaces. As a consequence, we recover and improve some compactness results for pseudodifferential operators.
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