Aljaž Zalar

activity

20102026

most citedMoment problems for operator polynomials

25 citations · 85 across the 22 of their papers we have counts for

collaborators

27 papers

math.FA2026

Operator Fejér--Riesz Theorems with Gaps and Degree Bounds

Abhay Jindal, Aljaž Zalar

Let $K$ be a nonempty compact semialgebraic subset of the real line, and let $S$ be a saturated scalar description of $K$ . We prove that every hermitian polynomial with bounded-ope…

math.FA2026

The Matricial Univariate Rational Truncated Moment Problem

Alja\v z Zalar, Igor Zobovi\v c

We solve the matricial univariate rational truncated moment problem on the real line and on a half-line. We give explicit necessary and sufficient conditions for the existence of a…

math.FA2026

Truncated Moment Problems and the Extension Property on Monomial Curves

Rajkamal Nailwal, Aljaž Zalar, Igor Zobovič

In several papers, Stochel and Szafraniec studied moment problems on algebraic sets from an operator-theoretic perspective, investigating when positive definite sequences satisfyin…

math.AG2026

Unobstructedness of affine Gorenstein terminal toric fourfolds

Matej Filip, Aljaž Zalar

We prove that every affine terminal Gorenstein toric variety of dimension at most four is unobstructed. In dimension four, the obstruction space need not vanish; instead, we determ…

math.ST2025

Maximal signed volume for (multivariate) supermodular quasi-copulas

Matjaž Omladič, Martin Vuk, Aljaž Zalar

Copulas are the primary tool for dependence modeling in statistics, and quasi-copulas are their essential companions. The latter appear, say, as infima or suprema of sets of copula…

math.FA2025

Cyclic polynomials in Dirichlet-type Spaces of the unit bidisk

Rajkamal Nailwal, Aljaž Zalar

For $α \in R,$ we consider the scale of function spaces, namely the Dirichlet-type space $D_{α}$ consisting of holomorphic functions on the unit bidisk $D^{2}$ , $f(z…

math.FA2025

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

Seonguk Yoo, Aljaž Zalar

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…

stat.ML2025

Extreme mass distributions for quasi-copulas

Matjaž Omladič, Martin Vuk, Aljaž Zalar

A recent survey, nicknamed "Hitchhiker's Guide", J.J. Arias-Garcıa, R. Mesiar, and B. De Baets, A hitchhiker's guide to quasi-copulas, Fuzzy Sets and Systems 393 (2020) 1-28, has r…

math.FA2024

Bivariate Truncated Moment Sequences with the Column Relation $X Y = X^{m} + q (X)$ , with $q$ of degree $m - 1$

Seonguk Yoo, Aljaz Zalar

When the algebraic variety associated with a truncated moment sequence is finite, solving the moment problem follows a well-defined procedure. However, moment problems involving in…

math.FA2024

Gaussian Quadratures with prescribed nodes via moment theory

Rajkamal Nailwal, Aljaž Zalar

Let $μ$ be a positive Borel measure on the real line and let $L$ be the linear functional on univariate polynomials of bounded degree, defined as integration with respect to $μ$ . I…

math.FA2024

The truncated univariate rational moment problem

Rajkamal Nailwal, Aljaž Zalar

Given a closed subset $K$ in $R$ , the rational $K$ -truncated moment problem ( $K$ -RTMP) asks to characterize the existence of a positive Borel measure $μ$ , supported on $K$ …

math.ST2024

Extreme values of the mass distribution associated with $d$ -quasi-copulas via linear programming

Matej Belšak, Matjaž Omladič, Martin Vuk +1

The recent survey published in Fuzzy Sets and Systems nicknamed ``Hitchhiker's Guide'' has raised the rating of quasi-copula problems in the dependence modeling community in spite…

math.FA2024

The truncated moment problem on reducible cubic curves I: Parabolic and Circular type relations

Seonguk Yoo, Aljaž Zalar

In this article we study the bivariate truncated moment problem (TMP) of degree $2 k$ on reducible cubic curves. First we show that every such TMP is equivalent after applying an af…

math.FA2024

Cross-positive linear maps, positive polynomials and sums of squares

Igor Klep, Klemen Šivic, Aljaž Zalar

A linear map $Φ$ between matrix spaces is called cross-positive if it is positive on orthogonal pairs $(U, V)$ of positive semidefinite matrices in the sense that $\langle U,V\rangl…

math.FA2023★ 2 cited

A random copositive matrix is completely positive with positive probability

Igor Klep, 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. The cone of copositive matrices strictly contains the con…

math.FA2021★ 4 cited

The truncated moment problem on the union of parallel lines

Aljaž Zalar

In this article we study the bivariate truncated moment problem (TMP) of degree $2 k$ on the union of parallel lines. First we present an alternative proof of Fialkow's solution \ci…

math.FA2021★ 6 cited

The strong truncated Hamburger moment problem with and without gaps

Aljaž Zalar

The strong truncated Hamburger moment problem (STHMP) of degree $(- 2 k_{1}, 2 k_{2})$ asks to find necessary and sufficient conditions for the existence of a positive Borel measure, suppo…

math.FA2020★ 5 cited

The truncated Hamburger moment problems with gaps in the index set

Aljaž Zalar

In this article we solve four special cases of the truncated Hamburger moment problem (THMP) of degree $2 k$ with one or two missing moments in the sequence. As corollaries we obtai…

math.FA2020

The Tracial Moment Problem on Quadratic Varieties

Abhishek Bhardwaj, Aljaz Zalar

The truncated moment problem asks to characterize finite sequences of real numbers that are the moments of a positive Borel measure on Rn. Its tracial analog is obtained by integra…

math.FA2016★ 12 cited

There are many more positive maps than completely positive maps

Igor Klep, Scott McCullough, Klemen Šivic +1

A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are…

math.FA2016★ 5 cited

The singular bivariate quartic tracial moment problem

Abhishek Bhardwaj, Aljaž Zalar

The (classical) truncated moment problem, extensively studied by Curto and Fialkow, asks to characterize when a finite sequence of real numbers indexes by words in commuting variab…

math.OA2016★ 24 cited

Operator Positivstellensätze for noncommutative polynomials positive on matrix convex sets

Aljaž Zalar

This article studies algebraic certificates of positivity for noncommutative (nc) operator-valued polynomials on matrix convex sets, such as the solution set $D_{L}$ , called a free H…

math.AG2015★ 1 cited

Matrix Fejér-Riesz theorem with gaps

Aljaž Zalar

The matrix Fejér-Riesz theorem characterizes positive semidefinite matrix polynomials on the real line $R$ . We extend a characterization to arbitrary closed semialgebraic…

math.OA2014

Integral representations of -representations of -algebras

Aljaž Zalar

Regular normalized $B (W_{1}, W_{2})$ -valued non-negative spectral measures introduced in \cite{Zalar2014} are in one-to-one correspondence with unital $*$ -representations $ρ:C(X,\mat…

Operator Fejér--Riesz Theorems with Gaps and Degree Bounds

The Matricial Univariate Rational Truncated Moment Problem

Truncated Moment Problems and the Extension Property on Monomial Curves

Unobstructedness of affine Gorenstein terminal toric fourfolds

Maximal signed volume for (multivariate) supermodular quasi-copulas

Cyclic polynomials in Dirichlet-type Spaces of the unit bidisk

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

Extreme mass distributions for quasi-copulas

Bivariate Truncated Moment Sequences with the Column Relation XY=Xm+q(X), with q of degree m−1

Gaussian Quadratures with prescribed nodes via moment theory

The truncated univariate rational moment problem

Extreme values of the mass distribution associated with d-quasi-copulas via linear programming

The truncated moment problem on reducible cubic curves I: Parabolic and Circular type relations

Cross-positive linear maps, positive polynomials and sums of squares

A random copositive matrix is completely positive with positive probability

The truncated moment problem on the union of parallel lines

The strong truncated Hamburger moment problem with and without gaps

The truncated Hamburger moment problems with gaps in the index set

The Tracial Moment Problem on Quadratic Varieties

There are many more positive maps than completely positive maps

The singular bivariate quartic tracial moment problem

Operator Positivstellensätze for noncommutative polynomials positive on matrix convex sets

Matrix Fejér-Riesz theorem with gaps

Integral representations of *-representations of *-algebras

Bivariate Truncated Moment Sequences with the Column Relation $X Y = X^{m} + q (X)$ , with $q$ of degree $m - 1$

Extreme values of the mass distribution associated with $d$ -quasi-copulas via linear programming

Integral representations of -representations of -algebras