The Truncated Moment Problem for Homogeneous Polynomials

Abstract

Let \(\mathcal{H}_{d,m}\) denote the real homogeneous polynomials in d variables of degree m. In the final chapter of the book we deal with the truncated moment problem for \(\mathcal{H}_{d,2n}\) on \(\mathbb{R}^{d}\), on the unit sphere S d−1, and on S+ d−1. Since S+ d−1 is a realization of the projective space \(\mathbb{P}^{d-1}(\mathbb{R})\), the latter is in fact the truncated projective moment problem. The existence problem in this case was considered in Sect. 17.2.