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SIGMA, 2014, Volume 10, 078, 9 pages (Mi sigma943)  

This article is cited in 3 scientific papers (total in 3 papers)

Some Noncommutative Matrix Algebras Arising in the Bispectral Problem

F. Alberto Grünbaum

Department of Mathematics, University of California, Berkeley, CA 94720 USA

Abstract: I revisit the so called “bispectral problem” introduced in a joint paper with Hans Duistermaat a long time ago, allowing now for the differential operators to have matrix coefficients and for the eigenfunctions, and one of the eigenvalues, to be matrix valued too. In the last example we go beyond this and allow both eigenvalues to be matrix valued.

Keywords: noncommutative algebras; bispectral problem.

DOI: https://doi.org/10.3842/SIGMA.2014.078

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Full text: http://www.emis.de/journals/SIGMA/2014/078/
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Bibliographic databases:

ArXiv: 1407.6458
MSC: 13N10; 16S32; 35P05
Received: May 1, 2014; in final form July 17, 2014; Published online July 24, 2014
Language:

Citation: F. Alberto Grünbaum, “Some Noncommutative Matrix Algebras Arising in the Bispectral Problem”, SIGMA, 10 (2014), 078, 9 pp.

Citation in format AMSBIB
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\by F.~Alberto~Gr\"unbaum
\paper Some Noncommutative Matrix Algebras Arising in the Bispectral Problem
\jour SIGMA
\yr 2014
\vol 10
\papernumber 078
\totalpages 9
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\crossref{https://doi.org/10.3842/SIGMA.2014.078}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Alex Kasman, “Bispectrality of $N$-Component KP Wave Functions: A Study in Non-Commutativity”, SIGMA, 11 (2015), 087, 22 pp.  mathnet  crossref
    2. Sakhnovich A., “Generalized Backlund Darboux Transformation (Gbdt): Conservation Laws, Rational Extensions and Bispectrality”, Seventh international workshop: group analysis of differential equations and integrable systems (gadeisvii), Journal of Physics Conference Series, 621, IOP Publishing Ltd, 2015, 012013  crossref  mathscinet  isi  scopus
    3. J. Geiger, E. Horozov, M. Yakimov, “Noncommutative bispectral Darboux transformations”, Trans. Am. Math. Soc., 369:8 (2017), 5889–5919  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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