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

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.

References in corpus (1)

• Polynomials with no zeros on the bidisk

Cited by in corpus (2)

• An inductive Julia-Caratheodory theorem for Pick functions in two variables
• On the continuation of locally operator monotone functions