Sturm‐Liouville eigenvalue problems on networks

The description of heat conduction on ramified wires, for instance, leads to a Sturm‐Liouville eigenvalue problem on a network. It is shown that these problems are special canonical eigenvalue problems in the sense of Hölder, and therefore they can be investigated within the theory of S ‐Hermitian eigenvalue problems. In particular, Wielandt's expansion theorem can be applied in order to obtain eigenfunction expansions.