h-Fourier Integral Operators with Complex Phase

Yıl 2018, Cilt: 6 Sayı: 1, 77 - 84, 27.04.2018

Chafika Amel Aitemrar Abderrahmane Senoussaoui

https://doi.org/10.36753/mathenot.421767

Öz

Anahtar Kelimeler

h-admissible Fourier integral operators, complex phase, boundedness, compactness, amplitude

Kaynakça

• [1] Aitemrar, C. A. and Senoussaoui, A., h-Admissible Foureir integral opertaors. Turk. J. Math., vol 40, 553-568, 2016.
• [2] Asada, K. and Fujiwara, D., On some oscillatory transformations in L^2(R^n). Japanese J. Math., vol 4 (2), 299-361, 1978.
• [3] Bekkara, B., Messirdi, B. and Senoussaoui, A., A class of generalized integral operators. Elec J. Diff. Equ., vol 2009, no.88, (2009), 1–7.
• [4] Calderón, A.P. and Vaillancourt, R., On the boundedness of pseudodifferential operators. J. Math. Soc. Japan, 23, 1971, p374-378.
• [5] Duistermaat, J.J., Fourier integral operators. Courant Institute Lecture Notes, New-York 1973.
• [6] Egorov, Yu.V., Microlocal analysis. In Partial Differential Equations IV. Springer-Verlag Berlin Heidelberg, p1-147, 1993.
• [7] Hasanov, M., A class of unbounded Fourier integral operators. J. Math. Anal. Appl., 225, 641-651, 1998.
• [8] Harrat, C. and Senoussaoui, A., On a class of h-Fourier integral operators. Demonstratio Mathematica, Vol. XLVII, No 3, 596-607, 2014.
• [9] Helffer, B., Théorie spectrale pour des opérateurs globalement elliptiques. Société Mathématiques de France, Astérisque 112, 1984.
• [10] Hörmander, L., Fourier integral operators I. Acta Math., vol 127, 1971, p79-183.
• [11] Hörmander, L., The Weyl calculus of pseudodifferential operators. Comm. Pure. Appl. Math., 32 (3), p359-443, 1979.
• [12] Messirdi, B. and Senoussaoui, A., On the L^2 boundedness and L^2compactness of a class of Fourier integral operators. Elec J. Diff. Equ., vol 2006, no.26, (2006), p1–12.
• [13] Messirdi, B. and Senoussaoui, A., Parametrix du problème de Cauchy C∞ muni d’un système d’ordres de Leray-Volevic.ˆ J. for Anal and its Appl., Vol 24, (3), 581–592, 2005.
• [14] Robert, D., Autour de l’approximation semi-classique. Birkäuser, 1987.
• [15] Senoussaoui, A., Opérateurs h-admissibles matriciels à symbole opérateur. African Diaspora J. Math., vol 4, (1), 7-26, 2007.