The partial trigonometric moment problem on an interval: The matrix case
Let \(\varphi_1, \varphi_2,\dots, \varphi_N\) be a sequence of \(p\times p\) matrices, and let \([- \omega,\omega]\subseteq [-\pi, \pi]\). The following partial trigonometric moment problem on an interval is considered: Characterize the set \(\mu(\omega)\) of all \(p\times p\) matrix- valued positive measures carried by \([-\omega, \omega]\) for which \(\varphi_k= \int^\pi_{-\pi} e^{-ikt} d\mu(t)\) for \(k= 0, 1,\dots, N\). In the scalar case \((p= 1)\) Akhiezer and Krein have proved this problem. Using a new approach, the authors solve the matrix version of the partial trigonometric moment problem on an interval in the nondegenerate case.
scientific article; zbMATH DE number 803716