Matrix-valued Hermitian Positivstellensatz, Lurking Contractions, and Contractive Determinantal Representations of Stable Polynomials

DOI10.1007/978-3-319-31383-2_7zbMath1377.47005arXiv1501.05527OpenAlexW1908474791MaRDI QIDQ5273435

Dmitry S. Kaliuzhnyi-Verbovetskyi, Anatolii Grinshpan, Hugo J. Woerdeman, Victor Vinnikov

Publication date: 6 July 2017

Published in: Operator Theory, Function Spaces, and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.05527

zbMATH Keywords

determinantal representationmultivariable polynomialstable polynomialclassical Cartan domainscontractive realizationpolynomially defined domain

Mathematics Subject Classification ID

Convex programming (90C25) Determinants, permanents, traces, other special matrix functions (15A15) Operator-theoretic methods (93B28) Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Applications of operator theory in systems, signals, circuits, and control theory (47N70) Solving polynomial systems; resultants (13P15)

Related Items

Contractive determinantal representations of stable polynomials on a matrix polyball, Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem, Amœbas and structural stability of multidimensional systems: a test algorithm based on Monte Carlo integration, Rational Inner Functions on a Square-Matrix Polyball, Bianalytic maps between free spectrahedra, Noncommutative polynomials describing convex sets, Bianalytic free maps between spectrahedra and spectraballs, Free noncommutative hereditary kernels: Jordan decomposition, Arveson extension, kernel domination