Let μ_Σ be the natural measure on R~N (N≥3) supported by a compact oriented analytic hypersurface Σ, ψ a smooth function on R~N and P(D) a differential operator in N variables of order m. We determine a sufficient condition on the number λ such that the Fourier integral of the distribution P(D)ψμ_Σ be summable by Cesàro means of order λ to zero in a point outside the hypersurface. This condition depends on m and on the position of the point with respect to the caustic of the hypersurface.
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