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Zeros of Gegenbauer-Sobolev Orthogonal Polynomials: Beyond Coherent Pairs

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Abstract

Iserles et al. (J. Approx. Theory 65:151–175, 1991) introduced the concepts of coherent pairs and symmetrically coherent pairs of measures with the aim of obtaining Sobolev inner products with their respective orthogonal polynomials satisfying a particular type of recurrence relation. Groenevelt (J. Approx. Theory 114:115–140, 2002) considered the special Gegenbauer-Sobolev inner products, covering all possible types of coherent pairs, and proves certain interlacing properties of the zeros of the associated orthogonal polynomials. In this paper we extend the results of Groenevelt, when the pair of measures in the Gegenbauer-Sobolev inner product no longer form a coherent pair.

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Authors and Affiliations

  1. DCCE, IBILCE, UNESP–Universidade Estadual Paulista, Rua Cristóvão Colombo 2265, 15054-000, São José do Rio Preto, SP, Brazil

    E. X. L. de Andrade, C. F. Bracciali & A. Sri Ranga

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  1. E. X. L. de Andrade
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  2. C. F. Bracciali
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  3. A. Sri Ranga
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Correspondence to A. Sri Ranga.

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This research is supported by grants from CNPq and FAPESP.

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de Andrade, E.X.L., Bracciali, C.F. & Sri Ranga, A. Zeros of Gegenbauer-Sobolev Orthogonal Polynomials: Beyond Coherent Pairs. Acta Appl Math 105, 65–82 (2009). https://doi.org/10.1007/s10440-008-9265-8

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  • DOI: https://doi.org/10.1007/s10440-008-9265-8

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