An inequality for polynomials with a prescribed zero |
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| Authors: | K. K. Dewan N. K. Govil |
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| Affiliation: | 1. Department of Mathematics, Jamia Millia Islmia, 11025, New Delhi, India
2. Department of Mathematics, Auburn University, 36849, Auburn, Al, USA
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| Abstract: | Letp n (z)=Σ k?0 n a k z k be a polynomial of degreen such that |p n (z)|≤M for |z|≤1. It is well, known that for 0≤u, $$|a_u | + |a_v | leqslant 4M/pi ,$$ , and this result is best possible. In this paper we sharpen the above inequlity for polynomialsp n (z) having a zero on |z|=1 or (more generally) if |p n (1)|=a. 0≤a≤1. |
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