On the application of one M.G.Krein's result to the spectral analysis of Sturm-Liouville operators

TL;DR

This paper applies Krein's theoretical results to advance the spectral analysis of Sturm-Liouville operators, exploring properties of related Dirac-type systems to derive new insights.

Contribution

It introduces novel applications of Krein's result to spectral analysis and studies properties of Dirac-type differential systems in this context.

Findings

New spectral analysis results for Sturm-Liouville operators

Properties of Dirac-type differential systems elucidated

Enhanced understanding of polynomial and eigenfunction relationships

Abstract

Discovered by M.G.Krein analogy between polinomials orthogonal on the unit circle and generalized eigenfunctions of certain differential systems is used to obtain some new results in the spectral analysis of Sturm-Liouville operators. Some properties of Dirac-type differential systems are studied.