Test Functions, Schur-Agler Classes and Transfer-Function Realizations: The Matrix-Valued Setting

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9 Citas (Scopus)

Resumen

Given a collection of test functions, one defines the associated Schur-Agler class as the intersection of the contractive multipliers over the collection of all positive kernels for which each test function is a contractive multiplier. We indicate extensions of this framework to the case where the test functions, kernel functions, and Schur-Agler-class functions are allowed to be matrix- or operator-valued. We illustrate the general theory with two examples: (1) the matrix-valued Schur class over a finitely-connected planar domain and (2) the matrix-valued version of the constrained Hardy algebra (bounded analytic functions on the unit disk with derivative at the origin constrained to have zero value). Emphasis is on examples where the matrix-valued version is not obtained as a simple tensoring with ℂN of the scalar-valued version.

Idioma originalInglés
Páginas (desde-hasta)529-575
Número de páginas47
PublicaciónComplex Analysis and Operator Theory
Volumen7
N.º3
DOI
EstadoPublicada - 1 jun 2013
Publicado de forma externa

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