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Fourier inversion of distributions supported by a hypersurface. (English) Zbl 1215.42017
The authors consider a compact oriented (N-1)-dimensional analytic submanifold Σ of N , with N3, and define the natural measure μ Σ on Σ, which can be seen as a distribution on N of order 0 and compact support included in Σ. In the main result, they give a sufficient condition in order that the Fourier integral of the distribution P(D)ψμ Σ at a point outside Σ is (C,λ)-summable to zero. Here P(D) is a partial differential operator with constant coefficients of order m and ψC ( N ,). As an example, they consider an ellipsoid Σ in 3 with axes of different lengths.
MSC:
42B10Fourier type transforms, several variables
46F12Integral transforms in distribution spaces
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