Positive one-point commuting difference operators
Gulnara S. Mauleshova, Andrey E. Mironov
TL;DR
This paper investigates positive one-point commuting difference operators, constructing explicit examples on hyperelliptic spectral curves, advancing understanding of their algebraic and spectral properties.
Contribution
It introduces new examples of positive one-point commuting difference operators on hyperelliptic spectral curves, expanding the class of known integrable difference operators.
Findings
Constructed explicit examples of such operators.
Analyzed their spectral curve properties.
Extended the theory of commuting difference operators.
Abstract
In this paper we study commuting difference operators containing a shift operator with only positive degrees. We construct examples of such operators in the case of hyperelliptic spectral curves.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Advanced Harmonic Analysis Research · Spectral Theory in Mathematical Physics