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We completely characterize the interior of the convex cone of finite sequences that have a representing measure on K.
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.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com