116 citations · 1.1k across the 72 of their papers we have counts for
75 papers
Convergence Rates for Lasserre's Upper-Bound Hierarchy on with Gaussian Measure
Sander Gribling, Igor Klep, Poornendu Kumar
We establish quantitative convergence rates for Lasserre's measure-based upper-bound hierarchy on using the standard Gaussian measure as the reference measure. For a…
Addendum to "Factoring non-negative operator valued trigonometric polynomials in two variables"
Michael A. Dritschel, Igor Klep, Scott McCullough +1
Factorization for positive semidefinite matrix-valued polynomials over a nonsingular compact affine real surface is established. Corollaries include Fejér-Riesz factorization for b…
Quantitative semidefinite certificates for ground-state energies of Pauli Hamiltonians
Igor Klep, Nando Leijenhorst, Victor Magron
The -local Hamiltonian problem is a central model for quantum many-body systems and Hamiltonian complexity. Semidefinite programming and noncommutative sum-of-squares hierarchie…
Operator-Valued Positivstellensätze on Matrix Convex Sets and Free Products of Finite Abelian Groups
Abhay Jindal, Igor Klep, Scott McCullough
We prove a Positivstellensatz for operator-valued noncommutative polynomials that are positive on matrix convex sets. Specifically, let be an operator-valued polynomial in $B(H…
Fejér--Riesz factorization for positive noncommutative trigonometric polynomials
Igor Klep, Jacob Levenson, Scott McCullough
We prove a Fejér-Riesz type factorization for positive matrix-valued noncommutative trigonometric polynomials on , where is either the…
Positive operator-valued noncommutative polynomials are squares
Abhay Jindal, Igor Klep, Scott McCullough
We establish operator-valued versions of the earlier foundational factorization results for noncommutative polynomials due to Helton (Ann.~Math., 2002) and one of the authors (Line…