Operator-valued Herglotz kernels and functions of positive real part on the ball (Q1958688)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Operator-valued Herglotz kernels and functions of positive real part on the ball |
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Operator-valued Herglotz kernels and functions of positive real part on the ball (English)
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4 October 2010
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Several subclasses of functions having positive real part in the unit ball in \(\mathbb C^d\) are examined. Main attention is paid to those functions which admit so called noncommutative Herglotz representation, that is, a representation where the integral of the Herglotz kernel with a measure is replaced by an operator-valued Herglotz kernel under a positive functional on the \(C^*\)-algebra.
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holomorphic functions in the unit ball
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positive real part
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Herglotz kernel
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operator-valued Herglotz formula
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\(C^{\ast}\)-algebra
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