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Hankel vector moment sequences and the non-tangential regularity at infinity of two variable Pick functions (1111.2075v2)

Published 8 Nov 2011 in math.CV and math.FA

Abstract: A Pick function of $d$ variables is a holomorphic map from $\Pid$ 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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