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For the truncated moment problem associated to a complex sequence γ(2n)={γij}i,j∈Z+,i+j⩽2n to have a representing measure μ, it is necessary for the moment matrix M(n) to be positive semidefinite, and for the algebraic variety Vγ to satisfy rankM(n)⩽cardVγ as well as a consistency condition: the Riesz functional vanishes on every polynomial of degree at most 2n that vanishes on Vγ. In previous work...
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