The \({\mathcal L}^ p\) space of a positive definite matrix of measures and density of matrix polynomials in \({\mathcal L}^ 1\)
The authors consider the space \(L^p(\mu)\), where \(1\leq p\leq\infty\) and \(\mu\) is a positive definite matrix of measures. The paper contains six theorems and ten lemmas. The main results are theorems which say that \(L^p_n(\mu)\) is a Banach (Hilbert) space for some \(p\) and that the set of all positive definite matrices of measures having the same moments as those of \(\mu\) is compact in the vague topology. Moreover, the authors give a density result for \(L^1(\mu)\) which is an extension to the matrix case of the well-known result.
scientific article; zbMATH DE number 1057418
scientific article