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Positive definite function
正定函數 (Positive-definite function)


A positive-definite function of a real variable x is a complex-valued function such that for any real numbers x1, …, xn the n × n matrix. is positive semi-definite (which requires A to be Hermitian; therefore f(−x) is the complex conjugate of f(x)).
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Lyapunov functions. 1 Positive Definite Functions & Quadratic Functions. Given a neighbourhood N of 0 ∈ Rn a function W : Rn → R is.
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作者:J Buescu被引用次数:8 — Positive definite functions have for long been known to satisfy the fol- lowing characterization. Theorem 1.1 (Bochner). A continuous function φ : R → C is ... Definition ... V(x) is a positive definite function, if the following conditions are satisfied (Guangren, 2004). ... Assume lim ‖ x ‖ → ∞ V ( ‖ x ‖ ) = ∞ ...
作者:A Hinrichs2011被引用次数:10 — Let f : R d → C be a bounded continuous function. We say that f is positive positive-definite, and if f is real valued, f ( x ) ≥ 0 for all x ∈ R d and there ...
作者:F Derrien2010被引用次数:3 — Clearly Ps ⊂ P. The class of positive definite functions is fully characterized by the Bochner's theorem [1]. Theorem 2.1. A function ϕ ∈ P if ...
作者:VP Zastavnyi2000被引用次数:87 — + is positive definite on. Rn is investigated; a criterion for positive definiteness of this function is given in terms of completely monotonic functions; ...
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作者:R Bhatia2015被引用次数:8 — Positive definite, conditionally negative definite, infin- itely divisible, operator monotone, completely monotone. 1. Page 4. 2. RAJENDRA BHATIA AND TANVI JAIN.
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