I need to verify whether a specified function f satisfies the (conditionally) negative-definite.

According to Bochner's theorem, a continuous real function −f(x) defined in R^n is positive definite if and only if it is the Fourier transform of a positive bounded Borel measure F(du); That is, I must take the Fourier transform of –f(x) and testify that it is positive bounded.

Now, I'm curious to learn :

1) whether there is an effective/efficient way to check for negative definiteness of a function?

2) Is there any numerical approximation method to see whether the Fourier transform of f has the positive bounded symmetric measure?

Definition: A function f:R^d→C is conditionally negative definite if f is conjugate symmetric, that is f(x)=f(−x) for all x∈R^d, and ∑f(x_i−x_j) v_i v_j ≤ 0, for all x_1,…,x_n ∈ R^d and v_1,…,v_n ∈ C satisfying ∑v_i=0, with any n∈N.