A Remark on Coefficients of Jacobi Matrices Arising from a Schrodinger Operator

TL;DR

This paper investigates the coefficients of a discrete Schrödinger operator with a singular continuous spectrum, revealing more complex behavior than previously conjectured, and provides insights into their properties.

Contribution

It answers a conjecture about the coefficients of a specific discrete Schrödinger operator, showing their behavior is more intricate than expected.

Findings

Coefficients exhibit more complex behavior than conjectured

The operator has a singular continuous spectrum

Provides new understanding of Jacobi matrix coefficients

Abstract

A discrete analogue of a Schrodinger type operator proposed by J. Bellissard has a singular continuous spectrum. In this remark we answer the conjecture formulated by D. Bessis, M. Mehta and P. Moussa on the coefficients of that operator. It turns out that the coefficients have a more complicated behavior than it was conjectured.