%0 Journal Article %T Hilbert-Schmidtness of Fourier integral operators in $\mathbf{SG}$ classes %J Khayyam Journal of Mathematics %I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures) %Z 2423-4788 %A Senoussaoui, Abderrahmane %A Aid, Omar Farouk %D 2023 %\ 01/01/2023 %V 9 %N 1 %P 144-152 %! Hilbert-Schmidtness of Fourier integral operators in $\mathbf{SG}$ classes %K Fourier integral operators %K SG symbol classes %K Hilbert-Schmidt operators %R 10.22034/kjm.2022.351589.2601 %X 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. %U https://www.kjm-math.org/article_164490_8835d5dda36598c04b28ad6138f8e5bb.pdf