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For a broad class of functions f: [0,+∞) → ℝ, we prove that the function f(ρλ(x)) is positive definite on a nontrivial real linear space E if and only if… Click to show full abstract
For a broad class of functions f: [0,+∞) → ℝ, we prove that the function f(ρλ(x)) is positive definite on a nontrivial real linear space E if and only if 0 ≤ λ ≤ α(E, ρ). Here ρ is a nonnegative homogeneous function on E such that ρ(x) ≢ 0 and α(E, ρ) is the Schoenberg constant.
Keywords:
related schoenberg;
schoenberg;
definiteness functions;
functions related;
positive definiteness;
schoenberg problem
Journal Title: Mathematical Notes
Year Published: 2017
Link to full text (if available)
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Journal Title: Mathematical Notes
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!