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Doklady Mathematics

, Volume 93, Issue 1, pp 62–64 | Cite as

One-point commuting difference operators of rank 1

  • G. S. MauleshovaEmail author
  • A. E. Mironov
Mathematics

Abstract

One-point commuting difference operators of rank 1 are considered. The coefficients in such operators depend on one functional parameter, and the degrees of shift operators in difference operators are positive. These operators are studied in the case of hyperelliptic spectral curves, where the base point coincides with a point of branching. Examples of operators with polynomial and trigonometric coefficients are constructed. Operators with polynomial coefficients are embedded in differential operators with polynomial coefficients. This construction provides a new method for constructing commutative subalgebras in the first Weyl algebra.

Keywords

Base Point Difference Operator Point Operator Spectral Curve Shift Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia
  2. 2.Sobolev Institute of Mathematics, Siberian BranchRussian Academy of SciencesNovosibirskRussia

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