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Several new properties of weighted Hilbert transform are obtained. If mu iszero, two Plancherel-like equations and the isotropic properties are derived.For mu is real number, a coerciveness is derived and two iterative sequencesare constructed to find the inversion. The proposed iterative sequences areapplicable to the case of pure imaginary constant mu=i*eta with |eta|<pi/4 .For mu=0.0 and 3.0 , we present the computer simulation results by using theChebyshev series representation of finite Hilbert transform. The results inthis paper are useful to the half scan in several imaging applications.

Finite Hilbert Transform in Weighted L2 Spaces