THE INVERSE PROBLEM FOR A SPECTRAL ASYMMETRY FUNCTION OF THE SCHRÖDINGER OPERATOR ON A FINITE INTERVAL

For the Schrödinger equation − d 2 u / x + q ( ) = λ on a finite x-interval, there is defined an “asymmetry function” ; , which entire of order 1/2 and type 1 in λ. Our main result identifies classes square-integrable potentials that possess common asymmetry function . any given one potential for each Dirichlet spectral sequence.