The boundary control method is shown to unify the Gelfand-Levitan, Krein, Simon, and Remling inverse spectral theories, yielding a local Gelfand-Levitan equation and an almost-everywhere spectral representation.
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The boundary control approach to inverse spectral theory
The boundary control method is shown to unify the Gelfand-Levitan, Krein, Simon, and Remling inverse spectral theories, yielding a local Gelfand-Levitan equation and an almost-everywhere spectral representation.