User:DVD206/Hilbert transfrom

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The Hilbert transform gives a correspondence between boundary values of harmonic function and its harmonic conjugate.


is an analytic function in the domain.

Exercise (*). Prove that for the case of the complex half-plane C+ the Hilbert transform is given by the following formula:

Exercise (*). Differentiate under integral sign the formula above to obtain the kernel representation for the Dirichlet-to-Neumann operator for the uniform half plane.

To define discrete Hilbert transform for a planar network, we need to consider it together w/its dual.