Equivalence of inverse Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter

By Paul Binding, P. Browne, B. Watson. 2004

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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 Prufer angle. For this it is necessary to produce direct results, of independent interest, on asymptotics and oscillation.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bb3109c5d29c9f547759b89e31864c0294175fa7