Inverse spectral problem for singular AKNS and Schrödinger operators on [formula omitted

Abstract

We consider an inverse spectral problem for singular Sturm–Liouville equations on the unit interval with explicit singularity a ( a + 1 ) / x 2 , a ∈ N . This problem arises by splitting of the Schrödinger operator with radial potential acting on the unit ball of R 3 . Our goal is the global parametrization of potentials by spectral data noted by λ a , and some norming constants noted by κ a . For a = 0 and 1, λ a × κ a was already known to be a global coordinate system on L R 2 ( 0 , 1 ) . We extend this to any non-negative integer a. Similar result is obtained for singular AKNS operator. To cite this article: F. Serier, C. R. Acad. Sci. Paris, Ser. I 340 (2005).