\displaystyle H_n = \left[ \begin{array}{cccc} m_0 & m_1 & \hdots & m_{n-1} \\ m_1 & m_2 & \hdots & m_n \\ \vdots & \vdots & \ddots & \vdots \\ m_{n-1} & m_n & \hdots & m_{2n-2} \end{array} \right]

with entries (H_n)_{i, j} = m_{i+j} is positive-definite. This is what I copy paste from your note.

Let us say we work in the range between \left[ 0,1\right]. What I am asking is that is there any way that for example we find the root of the Hankel determinants. Then for example the positivity of the Hankel determinant be grantee between \left[0, x \right] where x is the root we found in the previous step and then define the moments which have the hankel determinants at that range?

]]>Thanks for sharing your valuable information. I have a question. Here what I understand was that we have a set of moments and then we use the Hankel determinants to determines a faithful state of the moments (let us say the moments are realizable if they grantee the Hankel determinants to be positive). Now my main question is that is there a reverse algorithm for this problem? What I mean is that we find a moments space where the hankel determinants are absolutely positive and then choose our moment set from that range? Thanks in advance for your valuable comment . Best, Ehsan

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