Let $\{m_n\}_{n=0}^{\infty}$ be a sequence of real numbers.
It is well known that there exist a positive Borel measure $\mu$ on the real line with moments given by $\{m_n\}_{n=0}^{\infty}$ if and only if the Hankel matrix \begin{align} A=(m_{i+j})_{i,j=0}^\infty, \end{align}

is positive semi-definite.

In general the condition above condition can be difficult to verify.

My question: Is there a 'simpler' sufficient condition that can be checked?




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