Finite Hilbert Transform in Weighted L2 Spaces

Abstract: Several new properties of weighted Hilbert transform are obtained. If mu is zero, two Plancherel-like equations and the isotropic properties are derived. For mu is real number, a coerciveness is derived and two iterative sequences are constructed to find the inversion. The proposed iterative sequences are applicable 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 the Chebyshev series representation of finite Hilbert transform. The results in this paper are useful to the half scan in several imaging applications.