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Bispectral Algebras of Commuting Ordinary Differential Operators

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Abstract:

We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank N. It combines and unifies the ideas of Duistermaat–Grünbaum and Wilson. Our construction is completely algorithmic and enables us to obtain all previously known classes or individual examples of bispectral operators. The method also provides new broad families of bispectral algebras which may help to penetrate deeper into the problem.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Sofia University, 5 J. Bourchier Blvd., Sofia 1126, Bulgaria. E-mail: horozov@fmi.uni-sofia.bg, , , , , , BG

    B. Bakalov, E. Horozov & M. Yakimov

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  1. B. Bakalov
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  2. E. Horozov
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  3. M. Yakimov
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Received: 8 April 1996 / Accepted: 9 April 1997

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Bakalov, B., Horozov, E. & Yakimov, M. Bispectral Algebras of Commuting Ordinary Differential Operators . Comm Math Phys 190, 331–373 (1997). https://doi.org/10.1007/s002200050244

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  • DOI: https://doi.org/10.1007/s002200050244

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