Abstract
Given m > 0 and a finite collection of pairs of positive numbers C = {(α 1 (k),α 2 (k))}‖k‖≤m (‖k‖:= k 1 + k 2 ). 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 weighted are given by C. Curto and Fialkow solved this problem in the case m = 1, using the solution of truncated complex moment problem. This paper obtained the representing measure in detail.
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