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.
Senoussaoui, A., & Aid, O. F. (2023). Hilbert-Schmidtness of Fourier integral operators in $\mathbf{SG}$ classes. Khayyam Journal of Mathematics, 9(1), 144-152. doi: 10.22034/kjm.2022.351589.2601
MLA
Abderrahmane Senoussaoui; Omar Farouk Aid. "Hilbert-Schmidtness of Fourier integral operators in $\mathbf{SG}$ classes". Khayyam Journal of Mathematics, 9, 1, 2023, 144-152. doi: 10.22034/kjm.2022.351589.2601
HARVARD
Senoussaoui, A., Aid, O. F. (2023). 'Hilbert-Schmidtness of Fourier integral operators in $\mathbf{SG}$ classes', Khayyam Journal of Mathematics, 9(1), pp. 144-152. doi: 10.22034/kjm.2022.351589.2601
VANCOUVER
Senoussaoui, A., Aid, O. F. Hilbert-Schmidtness of Fourier integral operators in $\mathbf{SG}$ classes. Khayyam Journal of Mathematics, 2023; 9(1): 144-152. doi: 10.22034/kjm.2022.351589.2601