Two variable subnormal completion problem (Q1409280)

The two variable subnormal completion problem is to find necessary and sufficient conditions to guarantee the existence of a two variable subnormal weighted shift whose initial weights are given by a finite collection of pairs of positive numbers. \textit{R. E. Curto} and \textit{L. A. Fialkow} solved the above problem for a special case by using the solution of truncated complex moment problem [Integral Equations Oper. Theory 17, 202--246 (1993; Zbl 0804.47028); ibid. 18, 369--426 (1994; Zbl 0807.47016)]. In this paper, the author gives the representing measure in detail. In addition, two examples are given at the end of this paper.