A Pick function of variables is a holomorphic map from to , where is the upper halfplane. Some Pick functions of one variable have an asymptotic expansion at infinity, a power series with real numbers that gives an asymptotic expansion on non-tangential approach regions to infinity. In 1921 H. Hamburger characterized which sequences can occur. We give an extension of Hamburger's results to Pick functions of two variables.
Agler, Jim and McCarthy, John E., "Hankel vector moment sequences and the non-tangential regularity at infinity of two variable Pick functions" (2014). Mathematics Faculty Publications. 14.