Inverse spectral problems for left-definite Sturm–Liouville equations with indefinite weight

Inverse Sturm–Liouville problems with indefinite weight are considered. Theorems analogous to those of both Hochstadt and Gelfand–Levitan are proved. As a sample result, under suitable symmetry conditions, we show that half of one spectrum suffices to determine the potential function uniquely.  2002 Elsevier Science (USA). All rights reserved.