Weyl–Titchmarsh theory

Summary

Weyl–Titchmarsh theory is the spectral theory of singular Sturm–Liouville operators built on the Weyl–Titchmarsh function $m(z)$. The function $m$ records the boundary values of the square integrable solution of $-y'' + q y = z y$ at the regular end. It is a Herglotz function, and the measure in its integral representation is the spectral measure of the operator. So the spectrum, the eigenfunction expansion and, by the Borg–Marchenko theorem, even the potential $q$ can be read off from $m$. The theory goes back to Hermann Weyl and was developed by Edward Charles Titchmarsh.