Free Function Theory Through Matrix Invariants

DOI10.4153/CJM-2015-055-7zbMath1377.16017arXiv1407.7551OpenAlexW3105396244MaRDI QIDQ2981764

Igor Klep, Špela Špenko

Publication date: 10 May 2017

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.7551

zbMATH Keywords

free algebratrace identitiesinvariant theorypolynomial identitiesanalytic mapgeneralized polynomialsinverse function theoremconcomitantsfree analysis

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Trace rings and invariant theory (associative rings and algebras) (16R30) Noncommutative function spaces (46L52) Power series, series of functions of several complex variables (32A05)

Related Items (12)

Geometry of free loci and factorization of noncommutative polynomials ⋮ Function theory from tensor algebras ⋮ Operator noncommutative functions ⋮ Symmetric polynomials in free associative algebras ⋮ Non-commutative holomorphic functions on operator domains ⋮ Matrix coefficient realization theory of noncommutative rational functions ⋮ Local theory of free noncommutative functions: germs, meromorphic functions, and Hermite interpolation ⋮ Free holomorphic functions on the noncommutative polydomains and universal models ⋮ Bianalytic maps between free spectrahedra ⋮ Positive univariate trace polynomials ⋮ Bianalytic free maps between spectrahedra and spectraballs ⋮ Optimization over trace polynomials

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