Polynomial extremal problems in lp

E. B. Beller

doi:10.1090/S0002-9939-1971-0281884-9

Polynomial extremal problems in l^p

E. B. Beller

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

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Abstract

For p»2, letmp, n be the minimum of the L^p norm all nth degree polynomials Σⁿake^ikt ateikt which satisfy |ak| =1, k = 0, 1, ···, n. We exhibit certain polynomials Pn whose L^p norm(2<p<∞) is asymptotic to √n, thereby proving that mp, n is itself asymptotic to √n. We also show that the sup norm of (essentially) the same polynomials isasymptotic to (1.1716 …)X√n.

Original language	English
Pages (from-to)	249-259
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	30
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1971-0281884-9
State	Published - Oct 1971
Externally published	Yes

Keywords

Close to constant polynomials
Coefficients of constant modulus
Extremal polynomials
Fresnel integral
L norms of polynomials
Sup norm of polynomials
Van der corput's lemma

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10.1090/S0002-9939-1971-0281884-9

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KW - Close to constant polynomials

KW - Coefficients of constant modulus

KW - Extremal polynomials

KW - Fresnel integral

KW - L norms of polynomials

KW - Sup norm of polynomials

KW - Van der corput's lemma

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Polynomial extremal problems in l^p

Abstract

Keywords

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