It is shown formally how transmutation kernels can be characterized via a minimizing procedure. The technique then can be extended to more general operators and transmutations.

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R. Carroll and F. Santosa, “Spectral measures and autocorrelation via transmutation,” C. R. Roy. Soc. Canada (in press).
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This calculation suggests (as is indeed the case) that the characterization of K0 by minimization does not require the trace argument [i.e., the last integral in (2.3)];
the details will appear elsewhere.
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