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

Greg Knese

• Every two-variable rational inner function on the bidisk has a spe- cial 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 poly- disk. We study the class of rational inner functions on the poly- disk 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.