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The Darboux process and a noncommutative bispectral problem: some explorations and challenges

  • F. Alberto Grünbaum
Chapter
Part of the Progress in Mathematics book series (PM, volume 292)

Abstract

The Darboux process, also known by many other names, played a very important role in some extremely enjoyable joint work that Hans and I did many years ago. I revisit a version of this problem in a case when scalars are replaced by matrices, i.e., elements of a non-commutative ring. Many of the issues considered here can be pushed to the case of a ring with identity, but my emphasis is on very concrete examples involving 2×2 matrices. This paper could be seen as an invitation for further work.

Keywords

Darboux process matrix-valued orthogonal polynomials 

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© Springer Science+Buisness Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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