# An inverse spectral theory of Gel'fand-Levitan-type for higher order differential operators

Research paper by W. W. Zachary

Indexed on: 01 Sep '84Published on: 01 Sep '84Published in: Letters in Mathematical Physics

#### Abstract

An inverse spectral theory is presented for certain linear ordinary differential operators of arbitrary even order n which generalizes the Gel'fand-Levitan theory for Sturm-Liouville operators. It is proved that the coefficients in these operators are uniquely determined by n−1 distinct spectral matrices. Our method of proof makes use of a transformation due to M.K. Fage which generalizes the Povzner-Levitan transformations for Sturm-Liouville operators