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View all- Rueda SZurro M(2024)Spectral Curves for Third-Order ODOsAxioms10.3390/axioms1304027413:4(274)Online publication date: 20-Apr-2024
Computing Almost-Commuting Basis of Ordinary Differential Operators
Pages 111 - 118
Abstract
An effective computation of a basis of a nontrivial centralizer of a differential operator is the first step towards a Picard-Vessiot theory for spectral problems of ordinary differential operators. The set of almost-commuting operators enjoys a richer structure that allows the computation of these centralizers. We present a method to calculate a basis of almost-commuting operators. Its application to the computation of nontrivial centralizers is illustrated by examples.
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F. Gesztesy and H. Holden. Soliton equations and their algebrogeometric solutions: Volume 1, (1 + 1)-dimensional continuous models. Cambridge University Press, 79, 2003.
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F. A. Grünbaum. Commuting pairs of linear ordinary differential operators of orders four and six. Physica D, 31:424--433, 1988.
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J. J. Morales-Ruiz, S. Rueda, and M. Zurro. Spectral Picard-Vessiot fields for Algebro-geometric SchrÖdinger operators. Annales de l'Institut Fourier, 71(3):1287--1324, 2021.
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Association for Computing Machinery
New York, NY, United States
Publication History
Published: 13 December 2023
Published in SIGSAM-CCA Volume 57, Issue 3
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View all- Rueda SZurro M(2024)Spectral Curves for Third-Order ODOsAxioms10.3390/axioms1304027413:4(274)Online publication date: 20-Apr-2024
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