For functions on the tetrablock, membership in the new Schur-Agler class is equivalent to a positivity condition and to a unitary-colligation realization, yielding interpolation, extension, and corona theorems.
Agler, On the representation of certain holomorphic functions defined on a polydisc, in Topics in operator theory: Ernst D
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Function Theory on Tetrablock: Realization, Interpolation, Extension and Toeplitz Corona Theorem
For functions on the tetrablock, membership in the new Schur-Agler class is equivalent to a positivity condition and to a unitary-colligation realization, yielding interpolation, extension, and corona theorems.