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Local behaviour of polynomials |
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| Authors: | D. P. Dryanov M. A. Qazi Q. I. Rahman. |
| Affiliation: | Département de Mathématiques et de Statistique, Université de Montréal, Montréal H3C 3J7, Canada ; Department of Mathematics, Tuskegee University, Tuskegee, Alabama 36088 ; Département de Mathématiques et de Statistique, Université de Montréal, Montréal H3C 3J7, Canada |
| Abstract: | In this paper we study the local behaviour of a trigonometric polynomial  around any of its zeros in terms of its estimated values at an adequate number of freely chosen points in  . The freedom in the choice of sample points makes our results particularly convenient for numerical calculations. Analogous results for polynomials of the form  are also proved. |
| Keywords: | Trigonometric polynomials algebraic polynomials M. Riesz's interpolation formula Schur's inequality Bernstein's inequality |
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