An extremal problem for polynomials with a prescribed zero. II

Rahman, Q. I.; Schmeisser, G.

doi:10.1090/S0002-9939-1979-0518524-4

An extremal problem for polynomials with a prescribed zero. II
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by Q. I. Rahman and G. Schmeisser PDF

Proc. Amer. Math. Soc. 73 (1979), 375-378 Request permission

Abstract:

Improving upon an earlier estimate it is shown that if ${p_n}(z)$ is a polynomial of degree at most n such that ${p_n}(1) = 0$ and ${\max _{|z| = 1}}|{p_n}(z)| \leqslant 1$, then $|{p_n}(0)| < 1 - (1.03369)/n + O(1/{n^2})$.

References

Francis P. Callahan Jr., An extremal problem for polynomials, Proc. Amer. Math. Soc. 10 (1959), 754–755. MR 114902, DOI 10.1090/S0002-9939-1959-0114902-3
A. Giroux and Q. I. Rahman, Inequalities for polynomials with a prescribed zero, Trans. Amer. Math. Soc. 193 (1974), 67–98. MR 352427, DOI 10.1090/S0002-9947-1974-0352427-3
Problems in complex function theory, Bull. London Math. Soc. 4 (1972), 354–366. MR 480954, DOI 10.1112/blms/4.3.354
Q. I. Rahman and G. Schmeisser, Some inequalities for polynomials with a prescribed zero, Trans. Amer. Math. Soc. 216 (1976), 91–103. MR 399427, DOI 10.1090/S0002-9947-1976-0399427-7
Q. I. Rahman and Frank Stenger, An extremal problem for polynomials with a prescribed zero, Proc. Amer. Math. Soc. 43 (1974), 84–90. MR 333123, DOI 10.1090/S0002-9939-1974-0333123-0