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Radial parts of Haar measures and probability distributions on the space of rational matrix-valued functions
Yu. A. Neretinabcd a University of Vienna
b State Scientific Center of the Russian Federation - Institute for Theoretical and Experimental Physics, Moscow
c Lomonosov Moscow State University
d Institute for Information Transmission Problems, Russian Academy of Sciences
Abstract:
We consider the space $\mathcal C$ of conjugacy classes of the unitary group
$\mathrm U(n+m)$ with respect to a smaller unitary group $\mathrm U(m)$.
It is known that to every element of $\mathcal C$ we can canonically assign
a rational matrix-valued function (the Livshits characteristic function)
on the Riemann sphere. We find an explicit expression for the natural measure
on $\mathcal C$ obtained as the push-forward of the Haar measure
of $\mathrm U(n+m)$ in terms of characteristic functions.
Keywords:
inner functions, characteristic functions, Haar measure, Cayley transform, random functions.
Received: 28.10.2015
Citation:
Yu. A. Neretin, “Radial parts of Haar measures and probability distributions on the space of rational matrix-valued functions”, Izv. RAN. Ser. Mat., 80:6 (2016), 127–140; Izv. Math., 80:6 (2016), 1118–1130
Linking options:
https://www.mathnet.ru/eng/im8467https://doi.org/10.1070/IM8467 https://www.mathnet.ru/eng/im/v80/i6/p127
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Abstract page: | 401 | Russian version PDF: | 54 | English version PDF: | 21 | References: | 46 | First page: | 19 |
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