Binary Truncated Moment Problems and the Hadamard Product

Abstract

Up to the present day, the best solution we can get to the truncated moment problem (TMP) is probably the Flat Extension The- orem. It says that if the corresponding moment matrix of a moment sequence admits a rank-preserving positive extension, then the sequence has a representing measure. However, constructing a flat extension for most higher-order moment sequences cannot be executed easily because it requires to allow many parameters. Recently, the author has considered various decompositions of a moment matrix to find a solution to TMP in- stead of an extension. Using a new approach with the Hadamard product, the author would like to introduce more techniques related to moment matrix decompositions.