Some inequalities for polynomials with a prescribed zero

Authors:
Q. I. Rahman and G. Schmeisser

Journal:
Trans. Amer. Math. Soc. **216** (1976), 91-103

MSC:
Primary 30A04

MathSciNet review:
0399427

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a polynomial of degree *n*. Given that has a zero on the circle , we estimate and

**[1]**R. P. Boas Jr.,*Inequalities for functions of exponential type*, Math. Scand.**4**(1956), 29–32. MR**0085343****[2]**R. P. Boas Jr.,*Inequalities for polynomials with a prescribed zero*, Studies in mathematical analysis and related topics, Stanford Univ. Press, Stanford, Calif., 1962, pp. 42–47. MR**0150269****[3]**Francis P. Callahan Jr.,*An extremal problem for polynomials*, Proc. Amer. Math. Soc.**10**(1959), 754–755. MR**0114902**, 10.1090/S0002-9939-1959-0114902-3**[4]**A. Giroux and Q. I. Rahman,*Inequalities for polynomials with a prescribed zero*, Trans. Amer. Math. Soc.**193**(1974), 67–98. MR**0352427**, 10.1090/S0002-9947-1974-0352427-3**[5]**Peter D. Lax,*Proof of a conjecture of P. Erdös on the derivative of a polynomial*, Bull. Amer. Math. Soc.**50**(1944), 509–513. MR**0010731**, 10.1090/S0002-9904-1944-08177-9**[6]***Problems in complex function theory*, Bull. London Math. Soc.**4**(1972), 354–366. MR**0480954****[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**0333123**, 10.1090/S0002-9939-1974-0333123-0

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
30A04

Retrieve articles in all journals with MSC: 30A04

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1976-0399427-7

Keywords:
Polynomials with a prescribed zero,
trigonometric polynomial,
Chebyshev polynomial,
entire function of exponential type

Article copyright:
© Copyright 1976
American Mathematical Society