Commuting differential operators of rank 2 with polynomial coefficients

DOI10.1007/s10688-016-0128-1zbMath1349.16029arXiv1409.4058OpenAlexW2962821075MaRDI QIDQ302467

Vardan S. Oganesyan

Publication date: 8 July 2016

Published in: Functional Analysis and its Applications, Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.4058

zbMATH Keywords

nonlinear equationdifferential operatorKrichever-Novikov equationDixmier hypothesisfirst Weyl algebraoperator of nontrivial rank

Mathematics Subject Classification ID

General theory of ordinary differential operators (47E05) Rings of differential operators (associative algebraic aspects) (16S32)

Related Items (12)

The AKNS hierarchy and finite-gap Schrödinger potentials ⋮ On commuting ordinary differential operators with polynomial coefficients corresponding to spectral curves of genus two ⋮ Common eigenfunctions of commuting differential operators of rank 2 ⋮ Alternative proof of Mironov's results on commuting self-adjoint operators of rank 2 ⋮ An algorithm for construction of commuting ordinary differential operators by geometric data ⋮ Discretization of commuting ordinary differential operators of rank 2 in the case of elliptic spectral curves ⋮ Commuting differential operators of rank 2 with trigonometric coefficients ⋮ Commuting Krichever-Novikov differential operators with polynomial coefficients ⋮ Commuting differential operators of rank 2 with rational coefficients ⋮ Centralizers of rank one in the first Weyl algebra ⋮ Commuting ordinary differential operators and the Dixmier test ⋮ Commuting elements in the first Weyl algebra over \(\mathbb{Q} \)

Cites Work

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• Commuting ordinary differential operators of arbitrary genus and arbitrary rank with polynomial coefficients
• COMMUTING DIFFERENTIAL OPERATORS OF RANK 3, AND NONLINEAR DIFFERENTIAL EQUATIONS
• Commutative rings of ordinary linear differential operators
• Sur les algèbres de Weyl

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