Spectral density in a Moszynski's class of Jacobi matrices

TL;DR

This paper investigates the spectral density of a specific class of Jacobi matrices with absolutely continuous spectrum, showing it is generally equivalent to a positive continuous function except possibly at zero.

Contribution

It provides a detailed analysis of the spectral density for Moszynski's class of Jacobi matrices, clarifying its behavior across the spectrum.

Findings

Spectral density is equivalent to a positive continuous function almost everywhere.

Possible exception at the point x=0.

Extends understanding of spectral properties of Moszynski's Jacobi matrices.

Abstract

In this paper it is considered a spectral density for a class of Jacobi matrices with absolutely continuous spectrum that was examined first by Moszynski. It is shown that the corresponding spectral density is equivalent to the positive continuous function everywhere except maybe the point $x=0$.