The Extremal Truncated Moment Problem

@article{Curto2006TheET,
  title={The Extremal Truncated Moment Problem},
  author={Raul Curto and Lawrence A. Fialkow and Heiko M. M{\"o}ller},
  journal={Integral Equations and Operator Theory},
  year={2006},
  volume={60},
  pages={177-200}
}
Abstract.For a degree 2n real d-dimensional multisequence $$\beta \equiv \beta^{(2n)} = \{\beta_i\}_{i\in{Z}^{d}_{+},|i|\leq 2n}$$ to have a representing measure μ, it is necessary for the associated moment matrix $${\mathcal{M}}(n)(\beta)$$ to be positive semidefinite and for the algebraic variety associated to β, $${\mathcal{V}} \equiv {\mathcal{V}}_{\beta}$$, to satisfy rank $${\mathcal{M}}(n) \leq$$ card $${\mathcal{V}}$$ as well as the following consistency condition: if a polynomial $$p… CONTINUE READING

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