Conservative Structured Noncommutative Multidimensional Linear Systems

By Joseph A. Ball, Gilbert J. Groenewald, Tanit Malakorn. 2005

86 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7831e11e3d7c7f55babb9d983197be0654691e71

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Citations in the corpus

Global Holomorphic Functions in Several Noncommuting Variables (2015, unknown): “of bounded operators; Ball, Groenewald and Malakorn [10], in the context of extending realization formulas from functions of commuting operators to functions of non-commuting operators; Alpay and Kalyuzhnyi-Verbovetzkii [6] in the context of realization formulas for rational functions that are J-uni”
Pick Interpolation for free holomorphic functions (2013, background): “An nc-function is a graded function φ defined on a set D ⊆ M[d] such that i) If x, y, x⊕ y ∈ D, then φ(x⊕ y) = φ(x)⊕ φ(y). ii) If s ∈ Mn is invertible and x, s −1xs ∈ D ∩ Mdn then φ(s −1xs) = s−1φ(x)s. ∗Partially supported by National Science Foundation Grant DMS 1068830 †Partially supported by Nati”
Singularities of rational functions and minimal factorizations: The noncommutative and the commutative setting (2009, background): “A comprehensive study of noncommutative realization theory appears in [5,7,6]; these papers give a unified framework of structured noncommutative linear systems for different kinds of realization formulae.”
Matrix-J-unitary Non-commutative Rational Formal Power Series (2004, background): “trix-J-inner ones for the case J= Iq) belong to the non-commutative Schur–Agler class. For this case, we recover the theorem on unitary realizations for FPSs from the latter class which was obtain in [12]. Moreover, our Theorem 6.4 establishes the existence of a minimal, thus ﬁnite-dimensional, unit”
Interpolation and transfer-function realization for the noncommutative Schur-Agler class (2016, methodology): “In the original work of [21] the nc Schur-Agler class SAQ(U ,Y) (for the special case of linear Q(z) = ∑d k=1 Lkzk with coefficient matrices Lk satisfying some additional conditions which we need not go into here) was”
Free holomorphic functions on the unit ball of B(H)n (2006, background): “This class was extended to more general settings by Ball, Groenewald and Malakorn (see [4,5]), and by Muhly and Solel (see [24–26]).”
Noncommutative reproducing kernel Hilbert spaces (2016, background): “It is also closely connected with the functional calculus arising from plugging in freely noncommuting operators for the free indeterminates in a formal power series, making use of the tensor products for the operator multiplication in each term of the series (see [10]).”
Operator Theory on Noncommutative Domains (2007, unknown): “Along this line, we also mention the paper [19] of Ball, Groenewald, and Malakorn.”
Foundations of Free Noncommutative Function Theory (2012, background): “In systems and control, noncommutative rational functions and formal power series appear naturally as recognizable formal power series of the theory of automata and formal languages [66, 95, 96, 38, 39, 40, 26] and as transfer functions of multidimensional systems with evolution along the free monoi”
The implicit function theorem and free algebraic sets (2014, unknown): “Nc-functions have been studied for a variety of reasons: by Anderson [4] as a generalization of the Weyl calculus; by Taylor [20], in the context of the functional calculus for non-commuting operators; Popescu [14, 15, 16, 17], in the context of extending classical function theory to d-tuples of bou”