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2007 A special Gaussian rule for trigonometric polynomials
Aleksandar S. Cvetkovic, Gradimir V. Milovanovic, Marija P. Stanic
Banach J. Math. Anal. 1(1): 85-90 (2007). DOI: 10.15352/bjma/1240321558

Abstract

Abram Haimovich Turetzkii [Uchenye Zapiski, 1 (149) (1959), 31-55 (translation in English in East J. Approx. 11 (2005), 337-359)] considered interpolatory quadrature rules which have the following form $\int_0^{2\pi}f(x)w(x)d x\approx \sum_{\nu=0}^{2n}w_\nu f(x_\nu)$, and which are exact for all trigonometric polynomials of degree less than or equal to $n$. Maximal trigonometric degree of exactness of such quadratures is $2n$, and such kind of quadratures are known as quadratures of Gaussian type or Gaussian quadratures for trigonometric polynomials. In this paper we prove some interesting properties of a special Gaussian quadrature with respect to the weight function $w_m(x)=1+\sin mx$, where $m$ is a positive integer.

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Aleksandar S. Cvetkovic. Gradimir V. Milovanovic. Marija P. Stanic. "A special Gaussian rule for trigonometric polynomials." Banach J. Math. Anal. 1 (1) 85 - 90, 2007. https://doi.org/10.15352/bjma/1240321558

Information

Published: 2007
First available in Project Euclid: 21 April 2009

zbMATH: 1140.65096
MathSciNet: MR2350197
Digital Object Identifier: 10.15352/bjma/1240321558

Subjects:
Primary: 65D30
Secondary: 42A05

Keywords: Gaussian type quadratures , orthogonality , trigonometric polynomials of semi-integer degree

Rights: Copyright © 2007 Tusi Mathematical Research Group

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