An l1 extremal problem for polynomials

E. Beller; Bruce C. Berndt

doi:10.1090/S0002-9939-1971-0280688-0

An l₁ extremal problem for polynomials

E. Beller
, Bruce C. Berndt

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Let SKn be the maximum of the l₁ norm, Σⁿ|x_k|, of all nth degree polynomials satisfying |Σⁿc_kz^k| ≦ for |z| =1. We prove that M_n is asymptotic to √n, by exhibiting polynomials P_n (which are partial sums of certain Fourier series), whose l₁ norm is asymptotic to √n.

Original language	English
Pages (from-to)	474-481
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	29
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1971-0280688-0
State	Published - Aug 1971
Externally published	Yes

Keywords

Close to constant polynomials
Coefficients of close to constant modulus
Extremal polynomials
Partial sums of fourier series
U norm of polynomials
Upper bound for nth derivative

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10.1090/S0002-9939-1971-0280688-0

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abstract = "Let SKn be the maximum of the l1 norm, Σn|xk|, of all nth degree polynomials satisfying |Σnckzk| ≦ for |z| =1. We prove that Mn is asymptotic to √n, by exhibiting polynomials Pn (which are partial sums of certain Fourier series), whose l1 norm is asymptotic to √n.",

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KW - Close to constant polynomials

KW - Coefficients of close to constant modulus

KW - Extremal polynomials

KW - Partial sums of fourier series

KW - U norm of polynomials

KW - Upper bound for nth derivative

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An l₁ extremal problem for polynomials

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Keywords

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