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ALGEBRAIC STRUCTURE OF THE RANGE OF A TRIGONOMETRIC POLYNOMIAL
Part of
LEONID V. KOVALEV, XUERUI YANG
Journal:

Bulletin of the Australian Mathematical Society / Volume 102 / Issue 2 / October 2020

Published online by Cambridge University Press:

08 January 2020, pp. 251-260

Print publication:

October 2020
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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