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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, several variables 58J40 Pseudodifferential and Fourier integral operators on manifolds 44A15 Special transforms (Legendre, Hilbert, etc.)