Abstract
The spectral and inverse spectral theory for certain singular Sturm–Liouville problems is developed. These boundary value problems arise when considering the wave equation corresponding to a string with finitely many embedded point masses. These singular eigenvalue equations,their solutions, and the associated Hilbert space operators are constructed as limits of regular problems. The eigenfunctions of the singular problem are shown to be solutions of a regular eigenvalue problem with interior point conditions.Expressions describing the distribution of large eigenvalues are developed. Algorithms are given for extracting information about the singularities from eigenvalues corresponding to one or two sets of boundary conditions. In the generic case a single spectrum determines the (unordered) set of lengths of the intervals separating the singularities.
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