Solution of the Truncated Complex Moment Problem for Flat Data

In this book, the authors introduce a matricial approach to the truncated complex moment problem and apply it to the case of moment matrices of flat data type, for which the columns corresponding to the homogeneous monomials in $z$ and $\bar z$ of highest degree can be written in terms of monomials of lower degree. Necessary and sufficient conditions for the existence and uniqueness of representing measures are obtained in terms of positivity and extension criteria for moment matrices.