Zeros of Sobolev orthogonal polynomials of Gegenbauer type

JOURNAL OF APPROXIMATION THEORY

卷:114

Article

Groenevelt, WGM

关键词: Sobolev orthogonal polynomials;    symmetrically coherent pairs;    zeros;    Gegenbauer polynomials;   

DOI  :  10.1006/jath.2001.3643

来源: Elsevier

【 摘 要 】

Let {S-n}(n) denote the monic orthogonal polynomial sequence with respect to the Sobolev inner product (S) = integral f(x) g(x) dpsi(0)(x) + lambda integral f(x) g(x) dpsi(1)(x), where lambda<0 and {dpsi(0), dpsi(1)}is a so-called symmetrically coherent pair, with With dpsi(0) or dpsi(1) the classical Gegenbauer measure (x(2)- 1)(alpha)dx, alpha>- 1. If dpsi(1) is the Gegenbauer measure, then S-n has n different, real zeros. If dpsi(0) is the Gegenbauer measure, then S-n has at least n-2 different, real zeros. Under certain conditions S-n has complex zeros. Also the location of the zeros of S-n with respect to Gegenbauer polynomials, is studied. (C) 2002 Elsevier Science (USA).

【 授权许可】

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