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.