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The Bochner-Krall Problem: Some New Perspectives

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Special Functions 2000: Current Perspective and Future Directions

Part of the book series: NATO Science Series ((NAII,volume 30))

Abstract

The Bochner-Krall problem asks for the classification of all families of orthogonal polynomials that are also eigenfunctions of a differential operator. We survey some recent work on this problem. An important issue is to extend the problem by allowing for a doubly infinite three-term recursion relation, instead of a semi-infinite one. In this way, the problem gets connected with the associated classical orthogonal polynomials, the Darboux factorization method and the Burchnall-Chaundy theory of commutative rings of difference operators.

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Authors and Affiliations

  1. Department of Mathematics, Université Catholique de Louvain, Chemin du Cyclotron 2, 1348, Louvain-la-Neuve, Belgium

    Luc Haine

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  1. Luc Haine
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Editors and Affiliations

  1. Department of Mathematics, Arizona State University, Tempe, Arizona, USA

    Joaquin Bustoz  & Sergei K. Suslov  & 

  2. Department of Mathematics, University of South Florida, Tampa, Florida, USA

    Mourad E. H. Ismail

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Haine, L. (2001). The Bochner-Krall Problem: Some New Perspectives. In: Bustoz, J., Ismail, M.E.H., Suslov, S.K. (eds) Special Functions 2000: Current Perspective and Future Directions. NATO Science Series, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0818-1_7

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  • DOI: https://doi.org/10.1007/978-94-010-0818-1_7

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