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

Details 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

2011-11-08

arxiv.org/abs/1111.2075v2

Mathematics

Complex Variables

Scientific paper

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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