Periodic one-point rank one commuting difference operators

TL;DR

This paper investigates the conditions under which one-point rank one commutative rings of difference operators have periodic coefficients, advancing understanding of their spectral properties.

Contribution

It identifies specific spectral data conditions that characterize periodic one-point rank one commuting difference operators.

Findings

Derived conditions for spectral data of periodic operators

Characterized the structure of rank one commutative rings

Enhanced understanding of spectral theory for difference operators

Abstract

In this paper we study one-point rank one commutative rings of difference operators. We find conditions on spectral data which specify such operators with periodic coefficients.