On a class of h-Fourier integral operators with the complex phase
Resumo
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).
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Referências
K. Asada; D. Fujiwara. On some oscillatory transformation in L2 (Rn). Japan J. Math. vol 4, (2), 1978, p299-361. DOI: https://doi.org/10.4099/math1924.4.299
S. Bekkara, B. Messirdi, A. Senoussaoui, A class of generalized integral operators, Electron J. Differential Equations 88 (2009), 1–7.
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.
P. Drabek and J. Milota, Lectures on nonlinear analysis, Plezen, Czech Republic, 2004.
J. J. Duistermaat. Applications of Fourier Integral. Seminaire Goulaouic-S chwartz, 197, (1972).
J. J. Duistermaat. Fourier integral operators. Courant Institute Lecture Notes, New-York 1973.
M. Hasanov. A class of unbounded Fourier integral operators. Journal of Mathematical Analysis and Applications 225 (1998), 641-651. DOI: https://doi.org/10.1006/jmaa.1998.6033
C. Harrat and A. Senoussaoui, On a class of h-Fourier integral operators, Demonstratio Mathematica, Vol. XLVII, No. 3, 2014. DOI: https://doi.org/10.2478/dema-2014-0047
B. Helffer. Theorie spectrale pour des operateurs globalement elliptiques. Societe Mathematiques de France, Asterisque 112, 1984.
B. Helffer; J. Sjostrand. Multipes wells in the semiclassical limit I. Comm. P.D.E. vol 9 (4), 1984, p337-408. DOI: https://doi.org/10.1080/03605308408820335
L. Hormande. Linear partial differential operators. Springer-Verlag. Berlin, (1964). DOI: https://doi.org/10.1007/978-3-662-30724-3
L. Hormander. Fourier integral operators I. Acta Math. vol 127, 1971, p33-57. DOI: https://doi.org/10.1007/BF02392052
L. Hormander. The spectral function of an elliptic operator. Acta. Math., vol 121 (1968), p173-218. DOI: https://doi.org/10.1007/BF02391913
L. Hormander. The Weyl calculus of pseudodifferential operators. Comm. Pure. Appl. Math. 32 (1979), p359-443. DOI: https://doi.org/10.1002/cpa.3160320304
Melin, A and Sjostrand, J. Fourier integraux a phases complexes. Seminaire Equations aux derivees partielles (Poly-technique) (1973-1974)p 1-10.
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.
D. Robert. Autour de l’approximation semi-classique. Birkauser, 1987.
L. Rodino. Global hypoellipticity and spectral theory. Mathematical Researche vol. 92. Berlin, Akademic Verlag, 1996.
A. Senoussaoui, Operateurs h-admissibles matriciels a symbole operateur, African Diaspora J. Math. 4(1) (2007), 7–26.
J. Sjostrand. Singularites analytiques microlocales. Asterisque 95, 1982.
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