Sturm‐Liouville eigenvalue problems on networks

Abstract 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.