Open Access
2011 Rational inner functions in the Schur-Agler class of the polydisk
Greg Knese
Publ. Mat. 55(2): 343-357 (2011).


Every two-variable rational inner function on the bidisk has a special representation called a unitary transfer function realization. It is well known and related to important ideas in operator theory that this does not extend to three or more variables on the polydisk. We study the class of rational inner functions on the polydisk which do possess a unitary realization (the Schur-Agler class) and investigate minimality in their representations. Schur-Agler class rational inner functions in three or more variables cannot be represented in a way that is as minimal as two variables might suggest.


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Greg Knese. "Rational inner functions in the Schur-Agler class of the polydisk." Publ. Mat. 55 (2) 343 - 357, 2011.


Published: 2011
First available in Project Euclid: 22 June 2011

zbMATH: 1219.47028
MathSciNet: MR2839446

Primary: 47A57
Secondary: 42B05

Keywords: Agler decomposition , polydisk , reproducing kernel , Schur-Agler class , transfer function

Rights: Copyright © 2011 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.55 • No. 2 • 2011
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