Zeros of Gegenbauer-Sobolev Orthogonal Polynomials: Beyond Coherent Pairs

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...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2009, Vol.105 (1), p.65-82
Main Authors: de Andrade, E. X. L., Bracciali, C. F., Sri Ranga, A.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Computational Mathematics and Numerical Analysis
International
Mathematics
Mathematics and Statistics
Partial Differential Equations
Polynomials
Probability Theory and Stochastic Processes
Studies
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Summary: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.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-008-9265-8