Work

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

Year: 2026

Type: article

Abstract: 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.

Source: Banach Journal of Mathematical Analysis

DOI: 10.1007/s43037-026-00508-y

Authors: Seonguk Yoo, Aljaž Zalar

Institutions: Gyeongsang National University, University of Ljubljana, Institute of Mathematics, Physics, and Mechanics

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Javna Agencija za Raziskovalno Dejavnost RS