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Hankel vector moment sequences and the non-tangential regularity at infinity of two variable Pick functions

Hankel vector moment sequences and the non-tangential regularity at infinity of two variable Pick functions

A Pick function of $d$ variables is a holomorphic map from $\Pi ^d$ to $\Pi$, where $\Pi$ is the upper halfplane. Some Pick functions of one variable have an asymptotic expansion at infinity, a power series $\sum _{n=1}^\infty \rho _n z^{-n}$ with real numbers $\rho _n$ that gives an asymptotic …