Wave model of the regular Sturm-Liouville operator

We describe the wave functional model for the minimal (symmetric) Sturm-Liouville operator on the finite interval. We construct the wave spectrum of this operator, then, following the abstract scheme, we construct the model space of functions on the wave spectrum and introduce in that space the model operator. The latter is a matrix Sturm-Liouville operator which is unitarily equivalent to the original.