Iso-spectral operators: Some model examples with discontinuous coefficients (Q1118137)

Some explicit examples are presented of operators with different discontinuous coefficient functions which possess eigenvalue spectra identical to each other and to the corresonding operator with continuous coefficients. Cases covered include, for the second-order (Sturm- Liouville) problem, the vibrating stepped-density string and the circularly symmetric vibrations of a stepped, inverse-square density annular membrane. Fourth-order systems dealt with correspond to vibrating beams with various end-conditions.