I. Klep

发表

There are many more positive maps than completely positive maps

S. McCullough, I. Klep, Klemen vSivic, 2016, 1611.02838.

A Model Theoretic Perspective of Matrix Rings

Marcus Tressl, I. Klep, 2018, 1810.09024.

A note on the nonexistence of sum of squares certificates for the Bessis–Moussa–Villani conjecture

J. Povh, I. Klep, Kristijan Cafuta, 2010 .

A NOTE ON THE NONEXISTENCE OF SUM OF SQUARES CERTIFICATES FOR THE BMV CONJECTURE

J. Povh, I. Klep, Kristijan Cafuta, 2009 .

Free Function Theory Through Matrix Invariants

I. Klep, S. Spenko, 2014, Canadian Journal of Mathematics.

Noncommutative polynomials nonnegative on a variety intersect a convex set

J. Helton, I. Klep, Christopher S. Nelson, 2013, 1308.0051.

Convexity and Semidefinite Programming in Dimension-Free Matrix Unknowns

J. Helton, S. McCullough, I. Klep, 2012 .

FREE CONVEX ALGEBRAIC GEOMETRY

J. Helton, S. McCullough, I. Klep, 2013, 1304.4272.

Semidefinite programming in matrix unknowns which are dimension free

J. Helton, S. McCullough, I. Klep, 2011, 1112.6251.

Matrix convex hulls of free semialgebraic sets

J. Helton, S. McCullough, I. Klep, 2013, 1311.5286.

Positive trace polynomials and the universal Procesi–Schacher conjecture

J. Volčič, I. Klep, S. Spenko, 2017, Proceedings of the London Mathematical Society.

Dedicated to Bill Helton on the occasion of his ?? birthday

S. McCullough, I. Klep, Christopher S. Nelson, 2014 .

On trace-convex noncommutative polynomials

S. McCullough, I. Klep, Christopher S. Nelson, 2014, 1411.6636.

Optimization of Polynomials in Non-Commuting Variables

Igor Klep, Janez Povh, Sabine Burgdorf, 2016 .

Bianalytic maps between free spectrahedra

J. Helton, S. McCullough, I. Klep, 2016, 1604.04952.

Bianalytic free maps between spectrahedra and spectraballs

J. Helton, S. McCullough, I. Klep, 2018, Journal of Functional Analysis.

Free loci of matrix pencils and domains of noncommutative rational functions

I. Klep, Jurij Volvcivc, Jurij Volčič, 2015, 1512.02648.

Local theory of free noncommutative functions: germs, meromorphic functions, and Hermite interpolation

V. Vinnikov, I. Klep, Jurij Volvcivc, 2019, Transactions of the American Mathematical Society.

Geometry of free loci and factorization of noncommutative polynomials

J. Helton, I. Klep, Jurij Volvcivc, 2017, Advances in Mathematics.

Noncommutative partially convex rational functions

Michael T. Jury, Mark E. Mancuso, S. McCullough, 2020, Revista Matemática Iberoamericana.

Infeasibility certificates for linear matrix inequalities

M. Schweighofer, I. Klep, 2011, 1108.5930.

Factorization of Noncommutative Polynomials and Nullstellensätze for the Free Algebra

J. Helton, I. Klep, Jurij Volvcivc, 2019, International Mathematics Research Notices.

Free Analysis, Convexity and LMI Domains

J. Helton, S. McCullough, I. Klep, 2012, 1206.2401.

Cyclic Equivalence to Sums of Hermitian Squares

J. Povh, Sabine Burgdorf, I. Klep, 2016 .

Algorithmic aspects of sums of hermitian squares

J. Povh, Sabine Burgdorf, I. Klep, 2012 .

Sparse noncommutative polynomial optimization

J. Povh, I. Klep, Victor Magron, 2019, Mathematical Programming.

Classifying minimal vanishing sums of roots of unity.

K. Dykema, I. Klep, Louis Christie, 2020, 2008.11268.

Bianalytic maps between free spectrahedra

J. Helton, S. McCullough, I. Klep, 2018, Mathematische Annalen.

Optimization Over Trace Polynomials

J. Volčič, I. Klep, Victor Magron, 2021, Annales Henri Poincaré.

Dimension-Free Entanglement Detection in Multipartite Werner States

J. Volčič, I. Klep, Felix Huber, 2021, Communications in Mathematical Physics.

Constrained trace-optimization of polynomials in freely noncommuting variables

J. Povh, I. Klep, 2015, Journal of Global Optimization.

Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

J. Povh, Sabine Burgdorf, I. Klep, 2012, Computational Optimization and Applications.

The tracial moment problem and trace-optimization of polynomials

J. Povh, Sabine Burgdorf, I. Klep, 2011, Mathematical Programming.

Detecting Sums of Hermitian Squares

J. Povh, Sabine Burgdorf, I. Klep, 2016 .

Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem

Claus Scheiderer, J. Volčič, I. Klep, 2022, Mathematische Annalen.

The Noncommutative Graded Positivstellensatz

I. Klep, 2004 .

Noncommutative Polynomials Describing Convex Sets

J. Helton, S. McCullough, J. Volčič, 2020, Foundations of Computational Mathematics.

Selected Results from Algebra and Mathematical Optimization

J. Povh, Sabine Burgdorf, I. Klep, 2016 .

Multipartite Rational Functions

V. Vinnikov, I. Klep, Jurij Volvcivc, 2015, Documenta Mathematica.

Trace-positive polynomials

I. Klep, 2011 .

Eigenvalue Optimization of Polynomials in Non-commuting Variables

J. Povh, Sabine Burgdorf, I. Klep, 2016 .

The Real Spectrum of a Noncommutative Ring and the Artin-Lang Homomorphism Theorem

I. Klep, 2018 .

Regular and positive noncommutative rational functions

Igor Klep, James Eldred Pascoe, Jurij Volcic, 2016, J. Lond. Math. Soc..

Null- and Positivstellensätze for rationally resolvable ideals

V. Vinnikov, I. Klep, Jurij Volčič, 2015, 1504.08004.

Noncommutative rational functions invariant under the action of a finite solvable group

J. Pascoe, I. Klep, Gregor Podlogar, 2019, 1909.08043.

Embedding Ordered Valued Domains into Division Rings

I. Klep, 2007 .

Noncommutative Polynomials Describing Convex Sets

J. William Helton, Igor Klep, Scott McCullough, 2018, Found. Comput. Math..

Plurisubharmonic noncommutative rational functions

J. Helton, H. Dym, S. McCullough, 2019, 1908.01895.

A local-global principle for linear dependence of noncommutative polynomials

Igor Klep, Matej Brešar, I. Klep, 2011, 1103.1884.

Noncommutative ball maps

J. William Helton, Igor Klep, Scott McCullough, 2008, 0809.4874.

Ranks of linear matrix pencils separate simultaneous similarity orbits

H. Derksen, I. Klep, Jurij Volvcivc, 2021, Advances in Mathematics.

Skolem–Noether algebras

I. Klep, Christoph Hanselka, M. Brevsar, 2017, 1706.08976.

On real one-sided ideals in a free algebra

J. William Helton, Igor Klep, Scott McCullough, 2012, 1208.4837.

Non-Commutative Functional Calculus

J. Helton, S. McCullough, T. Malakorn, 2020, Operator Analysis.

Free Bianalytic Maps between Spectrahedra and Spectraballs in a Generic Setting

J. Helton, S. McCullough, I. Klep, 2017, Interpolation and Realization Theory with Applications to Control Theory.

FA ] 2 0 A ug 2 01 8 NONCOMMUTATIVE POLYNOMIALS DESCRIBING CONVEX SETS

J. Helton, S. McCullough, I. Klep, 2022 .

State polynomials: positivity, optimization and nonlinear Bell inequalities

I. Klep, Jie Wang, Victor Magron, 2023, 2301.12513.

Matrix Extreme Points and Free extreme points of Free spectrahedra

J. Helton, I. Klep, Eric Evert, 2022, 2212.00748.

Positive univariate trace polynomials

J. Pascoe, I. Klep, Jurij Volčič, 2020, 2009.10081.

Noncommutative Partial Convexity Via $$\Gamma $$ Γ -Convexity

Mark E. Mancuso, S. McCullough, J. Pascoe, 2019, The Journal of Geometric Analysis.

Extreme Points of Matrix Convex Sets, Free Spectrahedra, and Dilation Theory

J. Helton, S. McCullough, I. Klep, 2017, The Journal of Geometric Analysis.

The Tracial Hahn-Banach Theorem, Polar Duals, Matrix Convex Sets, and Projections of Free Spectrahedra

J. William Helton, Igor Klep, Scott McCullough, 2014, 1407.8198.

Extreme Points of Matrix Convex Sets, Free Spectrahedra, and Dilation Theory

J. Helton, S. McCullough, I. Klep, 2016, 1612.00025.

Circular free spectrahedra

J. Helton, S. McCullough, I. Klep, 2016, 1604.05756.

Constrained trace-optimization of polynomials in freely noncommuting variables

Igor Klep, Janez Povh, J. Povh, 2016, J. Glob. Optim..

Instances of the Kaplansky-Lvov multilinear conjecture for polynomials of degree three

K. Dykema, I. Klep, 2015, 1508.01238.

Proper analytic free maps

J. William Helton, Igor Klep, Scott McCullough, 2010, 1004.1381.

Analytic mappings between noncommutative pencil balls

J. William Helton, Igor Klep, Scott McCullough, 2009, 0908.0742.

Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions

J. William Helton, Igor Klep, Markus Schweighofer, 2014, Memoirs of the American Mathematical Society.

Trace-positive polynomials and the quartic tracial moment problem

Sabine Burgdorf, I. Klep, 2010 .

The truncated tracial moment problem

Igor Klep, Sabine Burgdorf, Sabine Burgdorf, 2010, 1001.3679.

Noncommutative Partial Convexity Via 0 -Convexity

Mark E. Mancuso, S. McCullough, J. Pascoe, 2019 .

The Prime Spectrum and the Extended Prime Spectrum of Noncommutative Rings

Marcus Tressl, I. Klep, 2007 .

The Joly-Becker theorem for orderings

I. Klep, Dejan Velušček, 2008 .

Central Extensions of *-ordered Skew Fields

I. Klep, Dejan Velušček, 2006 .

Central Extensions of n-Ordered Division Rings

I. Klep, Dejan Velušček, 2005 .

The matricial relaxation of a linear matrix inequality

J. William Helton, Igor Klep, Scott A. McCullough, 2010, Math. Program..

Relaxing LMI domination matricially

J. William Helton, Igor Klep, Scott A. McCullough, 2010, 49th IEEE Conference on Decision and Control (CDC).

Noncommutative Polynomial Optimization

Igor Klep, Victor Magron, Abhishek Bhardwaj, 2021, 2109.00786.

Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials

Igor Klep, Janez Povh, Kristijan Cafuta, 2013, Comput. Optim. Appl..

An Exact Duality Theory for Semidefinite Programming Based on Sums of Squares

Igor Klep, Markus Schweighofer, M. Schweighofer, 2012, Math. Oper. Res..

Constrained Polynomial Optimization Problems with Noncommuting Variables

Igor Klep, Janez Povh, Kristijan Cafuta, 2012, SIAM J. Optim..

The tracial moment problem and trace-optimization of polynomials

Igor Klep, Janez Povh, Kristijan Cafuta, 2013, Math. Program..

NCSOStools: a computer algebra system for symbolic and numerical computation with noncommutative polynomials

Igor Klep, Janez Povh, Kristijan Cafuta, 2011, Optim. Methods Softw..

Semidefinite programming and sums of hermitian squares of noncommutative polynomials

Igor Klep, Janez Povh, J. Povh, 2010 .

A Note on Group Representations, Determinantal Hypersurfaces and Their Quantizations

Igor Klep, Jurij Volčič, I. Klep, 2021 .

Noncommutative Nullstellensätze and Perfect Games

Igor Klep, Adam Bene Watts, John William Helton, 2021, Annales Henri Poincaré.

Values of noncommutative polynomials, Lie SkewIdeals and tracial Nullstellensätze

Igor Klep, Matej Bresar, I. Klep, 2008, 0810.1774.

A note on values of noncommutative polynomials

I. Klep, M. Brešar, 2009, 0909.2640.

Sign patterns for chemical reaction networks

Vitaly Katsnelson, Igor Klep, J. Helton, 2009, 0904.2960.

Connes' embedding conjecture and sums of hermitian squares

K. Dykema, M. Schweighofer, Sabine Burgdorf, 2006, 1303.3711.

The Procesi–Schacher conjecture and Hilbert's 17th problem for algebras with involution

I. Klep, T. Unger, 2008, 0810.5254.

On Valuations, Places and Graded Rings Associated to ∗-Orderings

I. Klep, 2007, Canadian Mathematical Bulletin.

Embedding ∗-ordered domains into skew fields

I. Klep, 2006 .

On -orderable groups

I. Klep, P. Moravec, 2005 .

The Real Spectrum of a Noncommutative Ring and the Artin-Lang Homomorphism Theorem

I. Klep, 2017, Algebras and Representation Theory.

The convex Positivstellensatz in a free algebra

J. William Helton, Igor Klep, Scott McCullough, 2011, 1102.4859.

Finite rings in which commutativity is transitive

I. Klep, P. Moravec, David Dolzan, 2011 .

Sums of squares certificates for polynomial moment inequalities

I. Klep, Jurij Volvcivc, Victor Magron, 2023, 2306.05761.

Optimization Over Trace Polynomials

Igor Klep, Victor Magron, Jurij Volvcivc, 2020, Annales Henri Poincaré.

Rational sums of hermitian squares of free noncommutative polynomials

Igor Klep, Janez Povh, Kristijan Cafuta, 2015, Ars Math. Contemp..

Determinant Expansions of Signed Matrices and of Certain Jacobians

J. William Helton, Igor Klep, Raul Gomez, 2008, SIAM J. Matrix Anal. Appl..

Minimizer Extraction in Polynomial Optimization Is Robust

Igor Klep, Janez Povh, Jurij Volcic, 2018, SIAM J. Optim..

State polynomials: positivity, optimization and nonlinear Bell inequalities

I. Klep, Jie Wang, Victor Magron, 2023, Math. Program..