On Fourier integral operators
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- Proc. Amer. Math. Soc. 85 (1982), 567-571 Request permission
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
- Lars Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79–183. MR 388463, DOI 10.1007/BF02392052 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.
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 567-571
- MSC: Primary 42B99; Secondary 35S05
- DOI: https://doi.org/10.1090/S0002-9939-1982-0660606-0
- MathSciNet review: 660606