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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?)

  • Lars Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79–183. MR 388463, DOI
  • F. Trêves, Pseudo-differential and Fourier integral operators, vols. 1 and 2, The University Series in Math., Plenum Press, New York, 1980. 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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Keywords: Fourier transform, operator, singular integral
Article copyright: © Copyright 1982 American Mathematical Society