Algebraic structure of the range of a trigonometric polynomial

Leonid V. Kovalev; Xuerui Yang

doi:10.1017/S0004972719001229

Algebraic structure of the range of a trigonometric polynomial

Leonid V. Kovalev, Xuerui Yang

Department of Mathematics

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

Abstract

The range of a trigonometric polynomial with complex coefficients can be interpreted as the image of the unit circle under a Laurent polynomial. We show that this range is contained in a real algebraic subset of the complex plane. Although the containment may be proper, the difference between the two sets is finite, except for polynomials with a certain symmetry.

Original language	English (US)
Pages (from-to)	251-260
Number of pages	10
Journal	Bulletin of the Australian Mathematical Society
Volume	102
Issue number	2
DOIs	https://doi.org/10.1017/S0004972719001229
State	Published - 2020

Keywords

Laurent polynomial
algebraic set
trigonometric polynomial

ASJC Scopus subject areas

General Mathematics

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10.1017/S0004972719001229

Cite this

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abstract = "The range of a trigonometric polynomial with complex coefficients can be interpreted as the image of the unit circle under a Laurent polynomial. We show that this range is contained in a real algebraic subset of the complex plane. Although the containment may be proper, the difference between the two sets is finite, except for polynomials with a certain symmetry.",

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Algebraic structure of the range of a trigonometric polynomial

Abstract

Keywords

ASJC Scopus subject areas

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