# The wave model of the Sturm-Liouville operator on an interval

## TL;DR

This paper develops a wave functional model for a symmetric restriction of the Sturm-Liouville operator on an interval, utilizing the wave spectrum concept, resulting in a transformed second-order differential operator.

## Contribution

It introduces a wave spectrum-based construction method for the Sturm-Liouville operator's symmetric restriction, providing a new functional model approach.

## Key findings

- Constructed a wave functional model for the operator
- Derived a differential operator differing by a simple transformation
- Extended the abstract scheme to Sturm-Liouville operators

## Abstract

In the paper we construct the wave functional model of a symmetric restriction of the regular Sturm-Liouville operator on an interval. The model is based upon the notion of the wave spectrum and is constructed according to an abstract scheme which was proposed earlier. The result of the construction is a differential operator of the second order on an interval, which differs from the original operator only by a simple transformation.