Direct and inverse Robin-Regge problems

Abstract

The Sturm-Liouville equation is considered on a bounded interval with a Robin boundary condition at the left end and a generalized Regge condition at the right end. Properties of the spectrum of this problem are derived, including the location of the spectrum in the lower half-plane and the asymptotic distribution of the eigenvalues. The inverse problem is solved, given one spectrum or parts of two spectra.

Keywords

• String problem
• viscous damping
• Robin boundary condition
• generalized Regge boundary condition
• spectral asymptotics
• inverse problems