The Nevanlinna parametrization for a matrix moment problem

  • Pedro Lopez-Rodriguez

Abstract

We obtain the Nevanlinna parametrization for an indeterminate matrix moment problem, giving a homeomorphism between the set $V$ of solutions to the matrix moment problem and the set $\mathcal V$ of analytic matrix functions in the upper half plane such that $V(\lambda )^*V(\lambda )\le I$. We characterize the N-extremal matrices of measures (those for which the space of matrix polynomials is dense in their $L^2$-space) as those whose corresponding matrix function $V(\lambda )$ is a constant unitary matrix.
Published
2001-12-01
How to Cite
Lopez-Rodriguez, P. (2001). The Nevanlinna parametrization for a matrix moment problem. MATHEMATICA SCANDINAVICA, 89(2), 245-267. https://doi.org/10.7146/math.scand.a-14340
Section
Articles