@article {
author = {Senoussaoui, Abderrahmane and Aid, Omar Farouk},
title = {Hilbert-Schmidtness of Fourier integral operators in $\mathbf{SG}$ classes},
journal = {Khayyam Journal of Mathematics},
volume = {9},
number = {1},
pages = {144-152},
year = {2023},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {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},
url = {https://www.kjm-math.org/article_164490.html},
eprint = {https://www.kjm-math.org/article_164490_8835d5dda36598c04b28ad6138f8e5bb.pdf}
}