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)).
作者：J BuescuPositive definite functions have for long been known to satisfy the fol- lowing characterization. Theorem 1.1 (Bochner). A continuous function φ : R → C is ... 被引用次数：8 —
126.96.36.199 Definition ... V(x) is a positive definite function, if the following conditions are satisfied (Guangren, 2004). ... Assume lim ‖ x ‖ → ∞ V ( ‖ x ‖ ) = ∞ ...
作者：A HinrichsLet 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 ... 2011 被引用次数：10 —
作者：F DerrienClearly Ps ⊂ P. The class of positive definite functions is fully characterized by the Bochner's theorem . Theorem 2.1. A function ϕ ∈ P if ... 2010 被引用次数：3 —
What does it mean for a function to be positive (semi)definite? Assume we have a positive (semi)definite function K(X,Y) that lives in Rn, and maps ...