h-Admissible Fourier integral operators

h-Admissible Fourier integral operators

We study in this work a class of h-admissible Fourier integral operators. These operators are bounded (respectively compact) in L 2 if the weight of the amplitude is bounded (respectively tends to 0).

___

  • [1] Asada K, Fujiwara D. On some oscillatory transformations in L 2 (R n ). Japanese J Math 1978; 4: 299-361.
  • [2] Bekkara S, Messirdi B, Senoussaoui A. A class of generalized integral operators. Elec J Diff Equ 2009; 88: 1-7.
  • [3] Calder´on AP, Vaillancourt R. On the boundedness of pseudodifferential operators. J Math Soc Japan 1971; 23: 374-378.
  • [4] Duistermaat JJ. Fourier Integral Operators. New York, NY, USA: Springer, 1973.
  • [5] Egorov YuV. Microlocal analysis. In: Partial Differential Equations IV: Berlin, Germany: Springer-Verlag, 1993, pp. 1-147.
  • [6] Hasanov M. A class of unbounded Fourier integral operators. J Math Anal Appl 1998; 225: 641-651.
  • [7] Harrat C, Senoussaoui A. On a class of h-Fourier integral operators. Demonstr Math 2014; XLVII: 596-607.
  • [8] Helffer B. Th´eorie spectrale pour des op´erateurs globalement elliptiques. Soci´et´e Math´ematiques de France: Ast ´erisque 112, 1984.
  • [9] H¨ormander L. Fourier integral operators I. Acta Math 1971; 127: 79-183.
  • [10] H¨ormander L. The Weyl calculus of pseudodifferential operators. Comm Pure Appl Math 1979; 32: 359-443.
  • [11] Messirdi B, Senoussaoui A. On the L 2 boundedness and L 2 compactness of a class of Fourier integral operators. Elec J Diff Equ 2006; 26: 1-12.
  • [12] Messirdi B, Senoussaoui A.Parametrix du probl`eme de Cauchy C ∞ muni d’un syst`eme d’ordres de Leray-Voleviˆc. Z. Anal. Anwendungen 2005; 24: 581-592.
  • [13] Robert D. Autour de l’Approximation Semi-classique. Secaucus, NJ, USA: Birkh¨auser, 1987.
  • [14] Senoussaoui A. Op´erateurs h-admissibles matriciels `a symbole op´erateur. African Diaspora J Math 2007; 4: 7-26.
  • [15] Senoussaoui A. On the unboundedness of a class of Fourier integral operators on L 2 (R n ). J Math Anal Appl 2013; 405: 700-705.