an:03905178
Zbl 0567.42010
Phong, D. H.; Stein, Elias M.
Singular integrals related to the Radon transform and boundary value problems
EN
Proc. Natl. Acad. Sci. USA 80, 7697-7701 (1983).
00147872
1983
j
42B20 58J40 44A15
Hilbert integral; manifold without boundary; hypersurface; singular density; Radon transform
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.
F.Natterer