Reconstruction of the solution of inverse Sturm–Liouville problem

Abstract

Abstract In this paper we are concerned with an inverse problem with Robin boundary conditions, which states that, when the potential on [ 0 , 1 / 2 ] $[0,1/2]$ and the coefficient at the left end point are known a priori, a full spectrum uniquely determines its potential on the whole interval and the coefficient at the right end point. We shall give a new method for reconstructing the potential for this problem in terms of the Mittag-Leffler decomposition of entire functions associated with this problem. The new reconstructing method also deduces a necessary and sufficient condition for the existence issue.

Keywords

• Eigenvalue
• Mittag-Leffler expansion
• Levin–Lyubarski interpolation theorem
• Reconstruction