, Volume 16, Issue 1, pp 34-51

Fourier Inversion of Distributions Supported by a Hypersurface

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Abstract

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)ψ μ 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.

Communicated by Tom Körner.