The Nevanlinna parametrization for a matrix moment problem | Zendy

Pedro Lopez-Rodriguez | Zendy

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The Nevanlinna parametrization for a matrix moment problem

Author(s) -

Pedro Lopez-Rodriguez

Publication year - 2001

Publication title -

mathematica scandinavica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.553

H-Index - 30

eISSN - 1903-1807

pISSN - 0025-5521

DOI - 10.7146/math.scand.a-14340

Subject(s) - mathematics , matrix (chemical analysis) , parametrization (atmospheric modeling) , moment (physics) , moment problem , lambda , matrix function , pure mathematics , combinatorics , mathematical analysis , symmetric matrix , eigenvalues and eigenvectors , statistics , physics , materials science , quantum mechanics , principle of maximum entropy , composite material , radiative transfer , classical mechanics , optics

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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