Abstract
AbstractLet and be a convergent multivariable power series in . In this paper, we present two conditions on the positive coefficients that imply that for nonnegative coefficients . If , then both of our results reduce to a lemma of Kaluza's. For , we present examples to show that our two conditions are independent of one another. It turns out that functions of the type satisfy one of our conditions, whenever is a product of probability measures on . Our results have applications to the theory of Nevanlinna–Pick kernels.
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