Aljavz Zalar

activity

20192026

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8 papers · 1 filter

math.FA2026

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…

math.FA2025

Matricial Gaussian quadrature rules: singular case

Aljaž Zalar, Igor Zobovič

Let $L$ be a linear operator on univariate polynomials of bounded degree taking values in real symmetric matrices, whose moment matrix is positive semidefinite. Assume that $L$ adm…

math.FA2025

Matricial Gaussian quadrature rules: nonsingular case

Aljaž Zalar, Igor Zobovič

Let $L$ 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 $…

math.FA2025

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…

math.FA2025

The pure $Y = X^{d}$ truncated moment problem

Lawrence Fialkow, Aljaž Zalar

Let $β \equiv β^{(2 n)}$ be a real bivariate sequence of degree $2 n$ . We study the existence of representing measures for $β$ supported in the curve $y = x^{d}$ ( $d \geq 1$ ) in the case w…

math.FA2025

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…

math.FA2025

Construction of exceptional copositive matrices

Tea Štrekelj, Aljaž Zalar

An $n \times n$ symmetric matrix $A$ is copositive if the quadratic form $x^{T} A x$ is nonnegative on the nonnegative orthant $R_{\geq 0}^{n}$ . The cone of copositive matrices…

math.FA2022

The truncated moment problem on curves $y = q (x)$ and $y x^{ℓ} = 1$

Aljaž Zalar

In this paper we study the bivariate truncated moment problem (TMP) on curves of the form $y = q (x)$ , $q (x) \in R [x]$ , $deg q \geq 3$ , and $y x^{ℓ} = 1$ , $\ell\in \mathb…

A constructive approach to the truncated moment problem on cubic curves in Weierstrass form

Matricial Gaussian quadrature rules: singular case

Matricial Gaussian quadrature rules: nonsingular case

Non-negative polynomials on generalized elliptic curves

The pure Y=Xd truncated moment problem

Matrix Fejér-Riesz type theorem for a union of an interval and a point

Construction of exceptional copositive matrices

The truncated moment problem on curves y=q(x) and yxℓ=1

The pure $Y = X^{d}$ truncated moment problem

The truncated moment problem on curves $y = q (x)$ and $y x^{ℓ} = 1$