A Property of the Ratio of Trigonometric Polynomials

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1964 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, volume 1, pages 131-132 (issn: 0887-459X,

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Authors: Rivlin, T. J.;

doi: 10.1137/0701011

A Property of the Ratio of Trigonometric Polynomials

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Abstract

The purpose of this note is to give a simple and relatively brief proof that it is possible to "factor out" zeros common to the numerator and de? nominator of a ratio of trigonometric polynomials. This result is needed in the paper of Cheney and Loeb [1, Lemma 9] where a different and longer proof is given. Let Tk be the set of trigonometric polynomials with real coefficients of proper degree k, i.e., t ? Tk , if, and only if,

Keywords

approximation and series expansion

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