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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Fourier integral operators


Author: A. El Kohen
Journal: Proc. Amer. Math. Soc. 85 (1982), 567-571
MSC: Primary 42B99; Secondary 35S05
MathSciNet review: 660606
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Abstract: We consider operators of the form: $ \int_{ - \infty }^\infty {{F_t}\varphi (t)\;dt} $, where $ {F_t}$ is a $ 1$-parameter family of Fourier integral operators and $ \varphi (t)\;dt$ a tempered distribution on the real line and show that these operators are sums of pseudo-differential and Fourier integral operators. Here, we give the typical case where $ \varphi (t)\;dt = {\text{p}}.{\text{v}}.\left\{ {1/t} \right\}$. An application to singular integrals on variable curves is given.


References [Enhancements On Off] (What's this?)

  • [1] Lars Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79–183. MR 0388463 (52 #9299)
  • [2] F. Trêves, Pseudo-differential and Fourier integral operators, vols. 1 and 2, The University Series in Math., Plenum Press, New York, 1980.
  • [3] S. Wainger and G. Weiss (Eds.), Proc. Sympos. Pure Math., Vol. 35, Part I, Amer. Math. Soc., Providence, R.I., 1979, pp. 95-98.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660606-0
PII: S 0002-9939(1982)0660606-0
Keywords: Fourier transform, operator, singular integral
Article copyright: © Copyright 1982 American Mathematical Society