Some spectral formulas for systems and transmission lines

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Abstract
The mathematical machinery for treating certain systems of equations arising from transmission line and geophysical problems is put into a transmutational framework involving canonical systems (∗) [JD- W]U = λU, and suitable spectral pairings of the solutions of (∗) with vectors involving Sinλt and Cosλt. One works with sideways and upward Cauchy problems, constructing solutions via such spectral pairings, and there by gives a spectral representation for the fundamental objects in the basic integral equations of scattering theory.