On orthogonal polynomials for certain nondefinite linear functionals

We consider the non-definite linear functionals L n[f]=∫ R w(x)f (n)(x) dx and prove the nonexistence of orthogonal polynomials, with all zeros real, in several cases. The proofs are based on the connection with moment preserving spline approximation.

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of computational and applied mathematics 1998-11, Vol.99 (1), p.119-128
1. Verfasser:	Ehrich, Sven
Format:	Artikel
Sprache:	eng
Schlagworte:	Exact sciences and technology Mathematical analysis Mathematics Measure and integration Moment preserving spline approximation Nondefinite linear functionals Nonexistence Orthogonal polynomials Sciences and techniques of general use Special functions
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Beschreibung
Zusammenfassung:	We consider the non-definite linear functionals L n[f]=∫ R w(x)f (n)(x) dx and prove the nonexistence of orthogonal polynomials, with all zeros real, in several cases. The proofs are based on the connection with moment preserving spline approximation.
ISSN:	0377-0427 1879-1778
DOI:	10.1016/S0377-0427(98)00150-2