The two-sided complex moment problem (Q910655)

A nicely written paper whose principle result is the following beautiful theorem \(({\mathbb{Z}}=integers\), \({\mathbb{C}}=complex\) numbers). Let \(({\mathbb{Z}}^ 2,+)\) be taken as a group with involution \((n,m)^*=(m,n)\). A function \(\phi\) : \({\mathbb{Z}}^ 2\to {\mathbb{C}}\) is positive definite if and only if there exists a Radon measure \(\mu\) on \({\mathbb{C}}-\{0\}\) such that for each \((n,m)\in {\mathbb{Z}}^ 2\), we have \(\int | z|^{n+m}d\mu (z)<\infty\) and \(\phi (n,m)=\int z^ n\bar z^ md\mu (z)\).