Book contents
- Frontmatter
- Contents of Volume 1
- Contents of Volume 2
- Integrable Systems: A Celebration of Emma Previato’s 65th Birthday
- 1 Trace Ideal Properties of a Class of Integral Operators
- 2 Explicit Symmetries of the Kepler Hamiltonian
- 3 A Note on the Commutator of Hamiltonian Vector Fields
- 4 Nodal Curves and a Class of Solutions of the Lax Equation for Shock Clustering and Burgers Turbulence
- 5 Solvable Dynamical Systems in the Plane with Polynomial Interactions
- 6 The Projection Method in Classical Mechanics
- 7 Pencils of Quadrics, Billiard Double-Reflection and Confocal Incircular Nets
- 8 Bi-Flat F-Manifolds: A Survey
- 9 The Periodic 6-Particle Kac-van Moerbeke System
- 10 Integrable Mappings from a Unified Perspective
- 11 On an Arnold-Liouville Type Theorem for the Focusing NLS and the Focusing mKdV Equations
- 12 Commuting Hamiltonian Flows of Curves in Real Space Forms
- 13 The Kowalewski Top Revisited
- 14 The Calogero-Franc¸oise Integrable System: Algebraic Geometry, Higgs Fields, and the Inverse Problem
- 15 Tropical Markov Dynamics and Cayley Cubic
- 16 Positive One–Point Commuting Difference Operators∗†
16 - Positive One–Point Commuting Difference Operators∗†
Published online by Cambridge University Press: 19 March 2020
Book contents
- Frontmatter
- Contents of Volume 1
- Contents of Volume 2
- Integrable Systems: A Celebration of Emma Previato’s 65th Birthday
- 1 Trace Ideal Properties of a Class of Integral Operators
- 2 Explicit Symmetries of the Kepler Hamiltonian
- 3 A Note on the Commutator of Hamiltonian Vector Fields
- 4 Nodal Curves and a Class of Solutions of the Lax Equation for Shock Clustering and Burgers Turbulence
- 5 Solvable Dynamical Systems in the Plane with Polynomial Interactions
- 6 The Projection Method in Classical Mechanics
- 7 Pencils of Quadrics, Billiard Double-Reflection and Confocal Incircular Nets
- 8 Bi-Flat F-Manifolds: A Survey
- 9 The Periodic 6-Particle Kac-van Moerbeke System
- 10 Integrable Mappings from a Unified Perspective
- 11 On an Arnold-Liouville Type Theorem for the Focusing NLS and the Focusing mKdV Equations
- 12 Commuting Hamiltonian Flows of Curves in Real Space Forms
- 13 The Kowalewski Top Revisited
- 14 The Calogero-Franc¸oise Integrable System: Algebraic Geometry, Higgs Fields, and the Inverse Problem
- 15 Tropical Markov Dynamics and Cayley Cubic
- 16 Positive One–Point Commuting Difference Operators∗†
Summary
In this paper we study a new class of rank one commuting difference operators containing a shift operator with only positive degrees. We obtain equations which are equivalent to the commutativity conditions in the case of hyperelliptic spectral curves. Using these equations we construct explicit examples of operators with polynomial and trigonometric coefficients.
- Type
- Chapter
- Information
- Integrable Systems and Algebraic Geometry , pp. 395 - 412Publisher: Cambridge University PressPrint publication year: 2020