Finite Hilbert Transform in Weighted L2 Spaces
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Several new properties of weighted Hilbert transform are obtained. If μ=0, two Plancherel-like equalities and the isotropic properties are derived. For μ>0, a coerciveness is established and two iterative sequences are constructed to find the inversion. The proposed iterative sequences are applicable to the case of pure imaginary constant μ=iη with η<π/4 . For μ=0.0 and 3.0 , we present the computer simulation results by using the discrete cosine and sine transforms. The results in this paper are useful to the image reconstruction in medical imaging applications.
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