Regular variation on homogeneous cones (Q2774615)
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scientific article; zbMATH DE number 1711084
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regular variation on homogeneous cones |
scientific article; zbMATH DE number 1711084 |
Statements
26 February 2002
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regularly varying function
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Regular variation on homogeneous cones (English)
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The author extends the notion of regular variation to functions defined on homogeneous cones in \({\mathbb R}^n\). (The theory of homogeneous cones was founded by \textit{E. B. Vinberg} [Tr. Mosk. Mat. Obshch. 12, 303-358 (1963; Zbl 0138.43301)] and \textit{S. G. Gindikin} [Usp. Mat. Nauk 19, No. 4(118), 3-92 (1964; Zbl 0144.08101)]). The Uniform Convergence Theorem and the Representation Theorem are proved as well as some facts about filters with respect to which the limit is taken in the definition of regular variation. Also, the relationship between ``multiplicative'' and ``additive'' regular variation in this setup is discussed.
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