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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Heun operator of Hahn-type
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by Luc Vinet and Alexei Zhedanov PDF
Proc. Amer. Math. Soc. 147 (2019), 2987-2998 Request permission

Abstract:

The Heun-Hahn operator on the uniform grid is defined. This operator is shown to map polynomials of degree $n$ to polynomials of degree $n+1$, to be tridiagonal in bases made out of either Pochhammer or Hahn polynomials, and to be bilinear in the operators of the Hahn algebra. The extension of this algebra that includes the Heun-Hahn operator as generator is described. Biorthogonal rational functions on uniform grids are shown to be related to this framework.
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Additional Information
  • Luc Vinet
  • Affiliation: Centre de recherches mathématiques, Université de Montréal, P.O. Box 6128, Centreville Station, Montréal, Québec, H3C 3J7 Canada
  • MR Author ID: 178665
  • ORCID: 0000-0001-6211-7907
  • Alexei Zhedanov
  • Affiliation: Department of Mathematics, School of Information, Renmin University of China, Beijing 100872, People’s Republic of China
  • MR Author ID: 234560
  • Received by editor(s): July 17, 2018
  • Received by editor(s) in revised form: October 10, 2018
  • Published electronically: March 7, 2019
  • Additional Notes: The research of the first author was funded in part by a discovery grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada.
    The work of the second author was supported by the National Science Foundation of China (Grant No.11771015).
  • Communicated by: Mourad Ismail
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 2987-2998
  • MSC (2010): Primary 33C45, 33C80, 39A70
  • DOI: https://doi.org/10.1090/proc/14425
  • MathSciNet review: 3973900