Rational inner functions in the Schur-Agler class of the polydisk

By Greg Knese. 2010

48 citations recorded by the source corpus.

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.

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

View Paper: https://www.semanticscholar.org/paper/37848206b68ca7006b00df766a6f598a49de1249

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In Algebra and Number Theory

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Operator monotone functions and L\"owner functions of several variables (2010, background): “tor monotone on the same set. What happens to Theorem 9.6 in d≥ 3 variables? It is still true that rational Lo¨wner functions have ﬁnite-dimensional models [11, 8]. However, a recent example of Knese [22] shows that the minimal dimension nr needed may be strictly greater than the degree of F in zr. ”