Fourier Inversion of Distributions Supported by a Hypersurface
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- González Vieli, F.J. & Seifert, E. J Fourier Anal Appl (2010) 16: 34. doi:10.1007/s00041-009-9073-1
Let μΣ be the natural measure on RN (N≥3) supported by a compact oriented analytic hypersurface Σ, ψ a smooth function on RN 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)ψμΣ 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.