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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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