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Singular integrals related to the Radon transform and boundary value problems. (English) Zbl 0567.42010
Let \(\Omega\) be a manifold without boundary and assume that through each point P in \(\Omega\) passes a hypersurface \(\Omega_ P\) that carries a singular density \(K_ P\). Given a function u, the singular Radon transform of u is the new function on \(\Omega\), whose value at P is the integral on \(\Omega_ P\) of u against \(K_ P\). Examples and applications arising from integral geometry and several complex variables are discussed.
Reviewer: F.Natterer

MSC:
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
58J40 Pseudodifferential and Fourier integral operators on manifolds
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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