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<p>This paper is concerned with the Chebyshev property for the trigonometric quasi-polynomials. We generalize the Derivation-Division algorithm to establish a criterion preserving the Chebyshev property of the union of Chebyshev families. By virtue of this criterion, we obtain several new Chebyshev families of quasi-polynomials and trigonometric quasi-polynomials. We also apply these families to the bifurcation analysis of a kind of differential equations, and partially improve the Khovanskiĭ theorem.</p>

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On the Study of the Chebyshev Property for the Families of Trigonometric Quasi-Polynomials via Generalized Derivation-Division Algorithm

  • 期刊论文

  • 发表日期：

    2025年3月28日

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  • Jianfeng Huang,
  • Yunyan Liu,
  • Jinfeng Li

摘要

This paper is concerned with the Chebyshev property for the trigonometric quasi-polynomials. We generalize the Derivation-Division algorithm to establish a criterion preserving the Chebyshev property of the union of Chebyshev families. By virtue of this criterion, we obtain several new Chebyshev families of quasi-polynomials and trigonometric quasi-polynomials. We also apply these families to the bifurcation analysis of a kind of differential equations, and partially improve the Khovanskiĭ theorem.