Hyperbolic distances in Hilbert spaces (Q1306323)
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scientific article; zbMATH DE number 1346970
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hyperbolic distances in Hilbert spaces |
scientific article; zbMATH DE number 1346970 |
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Hyperbolic distances in Hilbert spaces (English)
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22 February 2000
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Part of the rich contents of this paper is a functional equation characterization of the hyperbolic distance. Among other results offered we mention the equation \(H(X)=O(X) T(e) O(X)\), where \(X\) is a pre-Hilbert space, \(H(X)\) the hyperbolic group of \(X,\) \(O(X)\) is the group of all orthogonal mappings of \(X,\) and \(T(e)\) the group of all hyperbolic translations with axis \(e\).
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orthogonal mappings
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functional equations
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pre-Hilbert space
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Euclidean distance
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hyperbolic translations
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hyperbolic distance
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