Inverse spectral problems for Bessel operators

Abstract

We study the inverse spectral problem for a class of Bessel operators given in L 2 ( 0 , 1 ) by the differential expression − ( d d x − κ x − v ) ( d d x + κ x + v ) with κ ∈ N and a real-valued function v ∈ L p ( 0 , 1 ) , p ∈ [ 1 , ∞ ) , subject to various boundary conditions. We describe completely the spectral data of these operators, i.e., the spectra and corresponding norming constants, and give the algorithm of reconstruction of v from the spectral data.