Abstract
We obtain a qualitatively new sufficient condition of nonnegativity for the coefficients of a power series inverse to a series with positive coefficients. In particular, we prove that the element-wise product of the power series retains this property. In particular, this generalizes the classical Hardy–Kaluza theorem on power series. These results are generalized for the case of multivariable power series. Results of this kind are applied in the Nevanlinna–Pick theory.
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