On a class of h-Fourier integral operators with the complex phase
DOI:
https://doi.org/10.5269/bspm.42327Abstract
In this work, we study the L2-boundedness and L2-compactness of a class of h-Fourier integral operators with the complex phase. These operators are bounded (respectively compact) if the weight of the amplitude is bounded (respectively tends to 0).
References
1. K. Asada; D. Fujiwara. On some oscillatory transformation in L2 (Rn). Japan J. Math. vol 4, (2), 1978, p299-361.
2. S. Bekkara, B. Messirdi, A. Senoussaoui, A class of generalized integral operators, Electron J. Differential Equations 88 (2009), 1–7.
3. A. P. Calderon; R. Vaillancourt. On the boundness of pseudo-differential operators. J. Math. Soc. Japan 23, 1972, p374-378 bolicite. J.Math. Pures et Appl. 51 (1972), 231-256.
4. P. Drabek and J. Milota, Lectures on nonlinear analysis, Plezen, Czech Republic, 2004.
5. J. J. Duistermaat. Applications of Fourier Integral. Seminaire Goulaouic-S chwartz, 197, (1972).
6. J. J. Duistermaat. Fourier integral operators. Courant Institute Lecture Notes, New-York 1973.
7. M. Hasanov. A class of unbounded Fourier integral operators. Journal of Mathematical Analysis and Applications 225 (1998), 641-651.
8. C. Harrat and A. Senoussaoui, On a class of h-Fourier integral operators, Demonstratio Mathematica, Vol. XLVII, No. 3, 2014.
9. B. Helffer. Theorie spectrale pour des operateurs globalement elliptiques. Societe Mathematiques de France, Asterisque 112, 1984.
10. B. Helffer; J. Sjostrand. Multipes wells in the semiclassical limit I. Comm. P.D.E. vol 9 (4), 1984, p337-408.
11. L. Hormande. Linear partial differential operators. Springer-Verlag. Berlin, (1964).
12. L. Hormander. Fourier integral operators I. Acta Math. vol 127, 1971, p33-57.
13. L. Hormander. The spectral function of an elliptic operator. Acta. Math., vol 121 (1968), p173-218.
14. L. Hormander. The Weyl calculus of pseudodifferential operators. Comm. Pure. Appl. Math. 32 (1979), p359-443.
15. Melin, A and Sjostrand, J. Fourier integraux a phases complexes. Seminaire Equations aux derivees partielles (Poly-technique) (1973-1974)p 1-10.
16. B. Messirdi; A. Senoussaoui. On L2-boundness and L2-compactness of a class of Fourier integral operators, Electron J. Differential Equations 26 (2006), 1–12.
17. D. Robert. Autour de l’approximation semi-classique. Birkauser, 1987.
18. L. Rodino. Global hypoellipticity and spectral theory. Mathematical Researche vol. 92. Berlin, Akademic Verlag, 1996.
19. A. Senoussaoui, Operateurs h-admissibles matriciels a symbole operateur, African Diaspora J. Math. 4(1) (2007), 7–26.
20. J. Sjostrand. Singularites analytiques microlocales. Asterisque 95, 1982.
2. S. Bekkara, B. Messirdi, A. Senoussaoui, A class of generalized integral operators, Electron J. Differential Equations 88 (2009), 1–7.
3. A. P. Calderon; R. Vaillancourt. On the boundness of pseudo-differential operators. J. Math. Soc. Japan 23, 1972, p374-378 bolicite. J.Math. Pures et Appl. 51 (1972), 231-256.
4. P. Drabek and J. Milota, Lectures on nonlinear analysis, Plezen, Czech Republic, 2004.
5. J. J. Duistermaat. Applications of Fourier Integral. Seminaire Goulaouic-S chwartz, 197, (1972).
6. J. J. Duistermaat. Fourier integral operators. Courant Institute Lecture Notes, New-York 1973.
7. M. Hasanov. A class of unbounded Fourier integral operators. Journal of Mathematical Analysis and Applications 225 (1998), 641-651.
8. C. Harrat and A. Senoussaoui, On a class of h-Fourier integral operators, Demonstratio Mathematica, Vol. XLVII, No. 3, 2014.
9. B. Helffer. Theorie spectrale pour des operateurs globalement elliptiques. Societe Mathematiques de France, Asterisque 112, 1984.
10. B. Helffer; J. Sjostrand. Multipes wells in the semiclassical limit I. Comm. P.D.E. vol 9 (4), 1984, p337-408.
11. L. Hormande. Linear partial differential operators. Springer-Verlag. Berlin, (1964).
12. L. Hormander. Fourier integral operators I. Acta Math. vol 127, 1971, p33-57.
13. L. Hormander. The spectral function of an elliptic operator. Acta. Math., vol 121 (1968), p173-218.
14. L. Hormander. The Weyl calculus of pseudodifferential operators. Comm. Pure. Appl. Math. 32 (1979), p359-443.
15. Melin, A and Sjostrand, J. Fourier integraux a phases complexes. Seminaire Equations aux derivees partielles (Poly-technique) (1973-1974)p 1-10.
16. B. Messirdi; A. Senoussaoui. On L2-boundness and L2-compactness of a class of Fourier integral operators, Electron J. Differential Equations 26 (2006), 1–12.
17. D. Robert. Autour de l’approximation semi-classique. Birkauser, 1987.
18. L. Rodino. Global hypoellipticity and spectral theory. Mathematical Researche vol. 92. Berlin, Akademic Verlag, 1996.
19. A. Senoussaoui, Operateurs h-admissibles matriciels a symbole operateur, African Diaspora J. Math. 4(1) (2007), 7–26.
20. J. Sjostrand. Singularites analytiques microlocales. Asterisque 95, 1982.
Downloads
Published
2021-12-16
Issue
Section
Research Articles
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).
