Hilbert-Schmidtness of Fourier integral operators in $\mathbf{SG}$ classes

Document Type : Original Article

Authors

Abderrahmane Senoussaoui

Omar Farouk Aid

Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, Ahmed BEN BELLA. B.P. 1524 El M'naouar, Oran, Algeria

10.22034/kjm.2022.351589.2601

Abstract

In this paper, we define a particular class of Fourier integral operators with $\mathbf{SG}$-symbol. These class of operators turn out to be bounded on the spaces $\mathcal{S}\left(\mathbb{R}^{n}\right)$ of rapidly decreasing functions and turn out to be Hilbert-Schmidt on $L^2\left(\mathbb{R}^{n}\right)$. Mainly, we prove that the Fourier integral operators with $\mathbf{SG}$-symbol are a Hilbert-Schmidt operators.

Keywords

Fourier integral operators

SG symbol classes

Hilbert-Schmidt operators

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