Physical Sciences and Mathematics Commons^™

Hankel Vector Moment Sequences And The Non-Tangential Regularity At Infinity Of Two Variable Pick Functions, Jim Agler, John E. Mccarthy

Mathematics Faculty Publications

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.