Mate-Nevai-Totik theorem for Krein systems

TL;DR

This paper proves the Cesàro boundedness of Dirac operator eigenfunctions on the half-line with square-summable potentials, utilizing Krein systems and extending a classical theorem by Mate, Nevai, and Totik.

Contribution

It introduces a new application of Krein systems to establish boundedness properties of Dirac eigenfunctions, extending classical results to a continuous setting.

Findings

Eigenfunctions are Cesàro bounded for the Dirac operator with square-summable potential.

The proof leverages the theory of Krein systems and a continuous analogue of a classical theorem.

The result broadens understanding of spectral properties of Dirac operators with summable potentials.

Abstract

We prove the Ces\`aro boundedness of eigenfunctions of the Dirac operator on the half-line with a square-summable potential. The proof is based on the theory of Krein systems and, in particular, on the continuous version of a theorem by A. Mate, P. Nevai and V. Totik from 1991.