Isospectral sets for boundary value problems on the unit interval

Abstract

AbstractWe analyse isospectral sets of potentials associated to a given ‘generalized periodic’ boundary condition in SL(2, R) for the Sturm-Liouville equation on the unit interval. This is done by first studying the larger manifold M of all pairs of boundary conditions and potentials with a given spectrum and characterizing the critical points of the map from M to the trace a + d Isospectral sets appear as slices of M whose geometry is determined by the critical point structure of the trace function. This paper completes the classification of isospectral sets for all real self-adjoint boundary conditions.