Commuting differential operators of rank 2 with polynomial coefficients

Abstract

In this paper we study self-adjoint commuting ordinary differential operators with polynomial coefficients. These operators define commutative subalgebras of the first Weyl algebra. We find new examples of commuting operators of rank 2.

12 pages

References in corpus (3)

• Commuting ordinary differential operators with polynomial coefficients and automorphisms of the first Weyl algebra
• Common eigenfunctions of commuting differential operators of rank 2
• Commuting ordinary differential operators of arbitrary genus and arbitrary rank with polynomial coefficients

Cited by in corpus (9)

• Commuting ordinary differential operators with polynomial coefficients and automorphisms of the first Weyl algebra
• Commuting Ordinary Differential Operators and the Dixmier Test
• Common eigenfunctions of commuting differential operators of rank 2
• Explicit characterization of some commuting differential operators of rank 2
• Matrix commuting differential operators of rank 2
• Centralizers of Rank One in the First Weyl Algebra
• AKNS hierarchy and finite-gap Schrodinger potentials
• Commuting differential operators of rank 2 with rational coefficients
• On some questions around Berest's conjecture