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.

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DOI: http://dx.doi.org/10.7146/math.scand.a-14340

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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