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

Jim Agler; John E. McCarthy

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arXiv · 1111.2075

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

Jim Agler·John E. McCarthy

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Abstract

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 expansion on non-tangential approach regions to infinity. H. Hamburger in 1921 characterized which sequences $\{\rho_n\} $ can occur. We give an extension of Hamburger's results to Pick functions of two variables.

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Jim Agler, John E. McCarthy. 2011-11-08. Hankel vector moment sequences and the non-tangential regularity at infinity of two variable Pick functions. https://arxiv.org/abs/1111.2075

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