8 papers
A constructive approach to the truncated moment problem on cubic curves in Weierstrass form
Abhishek Bhardwaj, Aljaž Zalar
In this paper, we develop a constructive solution for the pure truncated moment problem on cubic curves in Weierstrass form, establishing the existence of a representing measure wh…
Matricial Gaussian quadrature rules: singular case
Aljaž Zalar, Igor Zobovič
Let be a linear operator on univariate polynomials of bounded degree taking values in real symmetric matrices, whose moment matrix is positive semidefinite. Assume that adm…
Matricial Gaussian quadrature rules: nonsingular case
Aljaž Zalar, Igor Zobovič
Let be a linear operator on univariate polynomials of bounded degree, mapping into real symmetric matrices, such that its moment matrix is positive definite. It is known that $…
Non-negative polynomials on generalized elliptic curves
Mario Kummer, Aljaž Zalar
We study the cone of non-negative polynomials on generalized elliptic curves. We show that the zero set of every extreme ray has dense real points. If a generalized elliptic curve…
The pure truncated moment problem
Lawrence Fialkow, Aljaž Zalar
Let be a real bivariate sequence of degree . We study the existence of representing measures for supported in the curve () in the case w…
Matrix Fejér-Riesz type theorem for a union of an interval and a point
Shengding Sun, Aljaž Zalar
The matrix Fejér-Riesz theorem characterizes positive semidefinite matrix polynomials on the real line. In the previous work of the second-named author this was extended to the cha…