On positivity of analytic matrix functions in polydisks - Bolotnikov, V.; Rodman, L. (Linear algebra and its applications, 2001)
We study analytic functions of several variables in the Korányi class such that, when applied to a contractive tuple of doubly commuting matrices, a positive definite matrix results. A criterion is given for a finite set to have the property that every measure supported on the set yields, via an integral formula, a function as above.