$h$-admissible Fourier integral operators with complex phase function
Abstract
e study in this work a particular class of $h$-admissible Fourier integral operators with complex phase function. These operators are bounded on Schwartz space $\mathcal{S}(\mathbb{R}^n)$ and on its dual $\mathcal{S}'(\mathbb{R}^n)$.
Downloads
References
Aid, O. F., Senoussaoui, A., The boundedness of h-admissible Fourier integral operators on Bessel potential spaces. Turk. J. Math., vol. 43, no. 5, pp. 2125 { 2141, 2019.
Aitemrar, C. A., Senoussaoui, A., h-Admissible Fourier integral operators. Turk. J. Math., vol 40, 553-568, 2016.
Aitemrar, C. A., Senoussaoui, A., h-Fourier Integral Operators with Complex Phase. Mathematical Sciences and Apllications E-Notes, 6 (1), 77-84, (2018).
Asada, K., Fujiwara,D., On some oscillatory transformations in L2 (Rn). Japanese J. Math., vol 4 (2), 299-361, 1978.
Duistermaat, J.J., Fourier integral operators. Courant Institute Lecture Notes, New-York 1973.
Egorov, Yu.V., Microlocal analysis. In Partial Differential Equations IV. Springer-Verlag Berlin Heidelberg, 1-147, 1993.
Eskin, Gregory I., Degenerate elliptic pseudodifferential equations of principal type. Mat. Sb. (N.S.), vol 82, 585-628, 1970.
Harrat, C., Senoussaoui, A., On a class of h -Fourier integral operators. Demonstratio Mathematica, Vol. XLVII, No 3, 596-607, 2014.
Hasanov, M., A class of unbounded Fourier integral operators. J. Math. Anal. Appl., 225, 641-651, 1998.
Helffer, B. Theorie spectrale pour des operateurs globalement elliptiques. Societe Mathematiques de France, Asterisque 112, 1984.
Hormander, L., Fourier integral operators I. Acta Math. vol 127, 79-183, 1971.
Hormander, L., Pseudo-differential Operators and Hypo-elliptic equations Proc. Symposium on Singular Integrals. Amer. Math. Soc. 10, 138183, 1967.
Messirdi, B., Senoussaoui, A., On the L2 boundedness and L2 compactness of a class of Fourier integral operators. Elec J. Diff. Equ., vol 2006, no.26, 1-12, 2006.
Messirdi, B., Senoussaoui, A., Parametrix du probleme de Cauchy C1 muni d'un systeme d'ordres de Leray-Volevic. J. for Anal and its Appl., Vol 24, (3), 581{592, 2005.
Robert, D., Autour de l'approximation semi-classique. Birkauser, 1987.
Senoussaoui, A., Operateurs h-admissibles matriciels a symbole operateur. African Diaspora J. Math. vol 4, (1), 7-26, 2007.
Copyright (c) 2024 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
