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Biorthogonal rational functions of $ R_{II}$-type


Authors: Kiran Kumar Behera and A. Swaminathan
Journal: Proc. Amer. Math. Soc. 147 (2019), 3061-3073
MSC (2010): Primary 41A20, 42C05, 15A18
DOI: https://doi.org/10.1090/proc/14443
Published electronically: March 15, 2019
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Abstract: In this work, a sequence of orthonormal rational functions leading to recurrence relations of $ R_{II}$-type is constructed. This sequence is proved to be biorthogonal to another sequence of rational functions as well. Two illustrations of such recurrence relations of $ R_{II}$-type, one through the associated linear pencil matrix leading to the -1 little Jacobi polynomials and the other through the bilinear transformation yielding the Bannai-Ito polynomials, which are orthogonal on the real line are exhibited.


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Additional Information

Kiran Kumar Behera
Affiliation: Department of Mathematics, Indian Institute of Technology, Roorkee-247667, Uttarakhand, India
Email: krn.behera@gmail.com

A. Swaminathan
Affiliation: Department of Mathematics, Indian Institute of Technology, Roorkee-247667, Uttarakhand, India
Email: mathswami@gmail.com, swamifma@iitr.ac.in

DOI: https://doi.org/10.1090/proc/14443
Keywords: Orthogonal rational functions, rational approximation, generalized eigenvalue problem, tridiagonal matrices, biorthogonality, Christoffel-type transform
Received by editor(s): May 8, 2018
Received by editor(s) in revised form: September 13, 2018, and October 20, 2018
Published electronically: March 15, 2019
Communicated by: Mourad Ismail
Article copyright: © Copyright 2019 American Mathematical Society