Krein systems with oscillating potentials

TL;DR

This paper establishes a fundamental equivalence between the mean decay of Krein system coefficients and the Fourier transform of its Szeg\

Contribution

It introduces a new equivalence linking decay properties of Krein system coefficients to Fourier transforms of associated functions.

Findings

Mean decay of Krein system coefficients is equivalent to Fourier transform decay.

Provides a new analytical tool for studying Krein systems.

Enhances understanding of spectral properties of oscillating potentials.

Abstract

We prove that mean decay of the coefficient of Krein system is equivalent to the mean decay of the Fourier transform of its Szeg\H{o} function.