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Quadrature Formulae and Polynomial Inequalities

✍ Scribed by A Guessab; Q.I Rahman

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 418 KB
Volume: 90
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1996.3080

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✦ Synopsis

In this paper we prove several inequalities for polynomials and trigonometric polynomials. They are all obtained as applications of certain quadrature formulae, some of which are proved here for the first time. Such an application of a Gaussian quadrature formula was pointed out by Bojanov in 1986 (see East. J. Approx. 1 (1995), 37 46; J. Approx. Theory 83 (1995), 175 181). Coincidentally, in the same year, it was shown how an inequality for entire functions of exponential type belonging to L 2 (R) could be deduced from a Gaussian quadrature formula for the doubly infinite integral & f (x) dx. 1997 Academic Press 1 &1 w * (x) ,(x) (x) dx, ( 2 ) article no. AT963080 255

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