no. 4
Estimates of one-dimensional oscillatory integrals
Annales de l'Institut Fourier, Tome 33 (1983) no. 4, pp. 189-201.

Nous considérons des intégrales oscillatoires, de dimension un, qui sont transformées de Fourier-Stieltjes de mesures suffisamment régulières à support compact sur des courbes indéfiniment dérivables dans des espaces euclidiens. Nous déterminons leur comportement à l’infini pourvu qu’ils satisfassent certaines conditions géométriques.

We study one-dimensional oscillator integrals which arise as Fourier-Stieltjes transforms of smooth, compactly supported measures on smooth curves in Euclidean spaces and determine their decay at infinity, provided the curves satisfy certain geometric conditions.

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     author = {Muller, Detlef},
     title = {Estimates of one-dimensional oscillatory integrals},
     journal = {Annales de l'Institut Fourier},
     pages = {189--201},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {33},
     number = {4},
     year = {1983},
     doi = {10.5802/aif.945},
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     mrnumber = {86f:42003},
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     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.945/}
}
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Muller, Detlef. Estimates of one-dimensional oscillatory integrals. Annales de l'Institut Fourier, Tome 33 (1983) no. 4, pp. 189-201. doi : 10.5802/aif.945. https://aif.centre-mersenne.org/articles/10.5802/aif.945/

[1] F. Carlson, Une inégalité, Ark. Mat. Astr. Fys., 25, B1 (1934). | JFM | Zbl

[2] L. Corwin, F. P. Greenleaf, Singular Fourier integral operators and representations of nilpotent Lie groups, Comm. on Pure and Applied Math., B1 (1978), 681-705. | MR | Zbl

[3] Y. Domar, On the Banach algebra A(Γ) for smooth sets Γ ⊂Rn, Comment. Math. Helv., 52 (1977), 357-371. | MR | Zbl

[4] C. S. Herz, Fourier transforms related to convex sets, Ann. of Math., (2), 75 (1962), 215-254. | MR | Zbl

[5] L. Hörmander, Lower bounds at infinity for solutions of differential equations with constant coefficients, Israel J. Math., 16 (1973), 103-116. | MR | Zbl

[6] W. Littman, Fourier transforms of surface-carried measures and differentiability of surface averages, Bull, Amer. Math. Soc., 69 (1963), 766-770. | MR | Zbl

[7] D. Müller, On the spectral synthesis problem for hypersurfaces of Rn, J. Functional Analysis, 47 (1982), 247-280. | Zbl

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