Algebraic structure of the range of a trigonometric polynomial

Leonid V. Kovalev, Xuerui Yang

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)251-260
Number of pages10
JournalBulletin of the Australian Mathematical Society
Volume102
Issue number2
DOIs
StatePublished - 2020

Keywords

  • Laurent polynomial
  • algebraic set
  • trigonometric polynomial

ASJC Scopus subject areas

  • Mathematics(all)

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