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Rational inner functions in the Schur-Agler class of the polydisk. (English) Zbl 1219.47028

Summary: 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.

MSC:

47A57 Linear operator methods in interpolation, moment and extension problems
42B05 Fourier series and coefficients in several variables
32A30 Other generalizations of function theory of one complex variable
32A70 Functional analysis techniques applied to functions of several complex variables
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