Wave model of the regular Sturm-Liouville operator

TL;DR

This paper develops a wave functional model for the symmetric Sturm-Liouville operator on a finite interval, constructing its wave spectrum and a unitary equivalent matrix operator to facilitate analysis.

Contribution

It introduces a novel wave spectrum construction and a model space for the Sturm-Liouville operator, providing a new framework for spectral analysis.

Findings

Constructed the wave spectrum of the Sturm-Liouville operator

Developed a model space of functions on the wave spectrum

Established a unitary equivalence to a matrix Sturm-Liouville operator

Abstract

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.