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arXiv · 1909.10345

Algebraic structure of the range of a trigonometric polynomial

Leonid V. Kovalev·Xuerui Yang
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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 certain symmetry.

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Leonid V. Kovalev, Xuerui Yang. 2019-09-23. Algebraic structure of the range of a trigonometric polynomial. https://doi.org/10.1017/s0004972719001229

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