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• W1521425374 abstract "<!-- *** Custom HTML *** --> Let <i>K</i> be an origin symmetric star body in ℝ^<i>n</i>. We prove, under very mild conditions on the function <i>f</i> : [0, ∞)→ℝ, that if the function <i>f</i>(‖<i>x</i>‖_<i>K</i>) is positive definite on ℝ^<i>n</i>, then the space (ℝ^<i>n</i>, ‖ ⋅ ‖_<i>K</i>) embeds isometrically in <i>L</i>₀. This generalizes the solution to Schoenberg’s problem and leads to progress in characterization of <i>n</i>-dimensional versions, i.e. random vectors <i>X</i>=(<i>X</i>₁, …, <i>X</i>_<i>n</i>) in ℝ^<i>n</i> such that the random variables ∑<i>a</i>_<i>i</i><i>X</i>_<i>i</i> are identically distributed for all <i>a</i>∈ℝ^<i>n</i>, up to a constant depending on ‖<i>a</i>‖_<i>K</i> only." @default.
• W1521425374 created "2016-06-24" @default.
• W1521425374 creator A5020408840 @default.
• W1521425374 date "2009-01-01" @default.
• W1521425374 modified "2023-09-26" @default.
• W1521425374 title "A note on positive definite norm dependent functions" @default.
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• W1521425374 doi "https://doi.org/10.1214/09-imscoll502" @default.
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