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?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.