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<p>In this paper, we solve <i>constructively</i> the bivariate truncated moment problem (TMP) of even degree on reducible cubic curves, where the conic part is a hyperbola. According to the classification from our previous work, these represent three out of nine possible canonical forms of reducible cubic curves after applying an affine linear transformation. Constructive solutions to the TMP on the union of three parallel lines and to the circular- and parabolic-type cases of the TMP are known, while in this paper we consider three hyperbolic-type cases, namely, a type without real self-intersection points, a type with a simple real self-intersection point, and a type with a double real self-intersection point. In all cases, we also establish bounds on the number of atoms in a minimal representing measure.</p>

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Constructive approach to the truncated moment problem on reducible cubic curves: hyperbolic-type relations

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  • 发表日期：

    2026年7月28日

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  • Seonguk Yoo,
  • Aljaž Zalar

摘要

In this paper, we solve constructively the bivariate truncated moment problem (TMP) of even degree on reducible cubic curves, where the conic part is a hyperbola. According to the classification from our previous work, these represent three out of nine possible canonical forms of reducible cubic curves after applying an affine linear transformation. Constructive solutions to the TMP on the union of three parallel lines and to the circular- and parabolic-type cases of the TMP are known, while in this paper we consider three hyperbolic-type cases, namely, a type without real self-intersection points, a type with a simple real self-intersection point, and a type with a double real self-intersection point. In all cases, we also establish bounds on the number of atoms in a minimal representing measure.