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arXiv · 1512.05560

Rational $q\times q$ Carathéodory Functions and Central Non-negative Hermitian Measures

Bernd Fritzsche·Bernd Kirstein·Conrad Mädler
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Abstract

We give an explicit representation of central measures corresponding to finite Toeplitz non-negative definite sequences of complex $q\times q$ matrices. Such measures are intimately connected to central $q\times q$ Carathéodory functions. This enables us to prove an explicit representation of the non-stochastic spectral measure of an arbitrary multivariate autoregressive stationary sequence in terms of the covariance sequence.

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Bernd Fritzsche, Bernd Kirstein, Conrad Mädler. 2015-12-17. Rational $q\times q$ Carathéodory Functions and Central Non-negative Hermitian Measures. https://arxiv.org/abs/1512.05560

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