Abstract
Three inverse problems for a Sturm–Liouville boundary value problem − y″+ qy= λy, y(0)cos α= y′(0)sin α and y′(1)= f( λ) y(1) are considered for rational f. It is shown that the Weyl m-function uniquely determines α, f, and q, and is in turn uniquely determined by either two spectra from different values of α or by the Prüfer angle. For this it is necessary to produce direct results, of independent interest, on asymptotics and oscillation.
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