Some features of the maps from potential to spectral data

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Abstract
Some significant spectral quantities for half line impedance problems are displayed and studied as functions of the appropriate potentials. Localizations (Frechet derivatives) are obtained in terms of products of einenfunctions; a systematic development of Marčenko (M) equations is given with recovery formulas for potentials via spectral traces of transmutation kernels containing appropriate spectral data; a spectral trace deduced from calculations with Gelfand-Levitan (G-L) kernels containing suitable spectral data leads to formulas for a kind of spectral transform (IST) extending the Sine transform with products of einenfunctions in the kernels

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