Rational Functions with a General Distribution of Poles on the Real Line Orthogonal with Respect to Varying Exponential Weights: I

Construction of the Solution of the Inverse Spectral Problem for a System Depending Rationally on the Spectral Parameter, Borg–Marchenko-Type Theorem and Sine-Gordon Equation

“…Different generalizations of the notion of a Weyl function are based on the asymptotics of the fundamental solution (see e.g. [4,5,11,18,22,27,28,34,36,48,50]). …”