Absolutely continuous representing measures of moment functionals: the general truncated case

In this work, we investigate and characterize linear functionals L: V R[x₁, ,xₙ]→ R L : V ⊊ R [ x 1 , ⋯ , x n ] → R with finite-dimensional V V and absolutely continuous representing measures μ μ , i.e., dμ (x) = g(x)\,dx d μ ( x ) = g ( x ) d x for some density g . We focus on the regularity of the density g .