In general, for proving that the given kernel function is valid, I try one of the following two approaches:
Check if the gram matrix is Symmetric Postive Semi Definite.
Check if the kernel function can be expressed in terms of other functions by using closure properties of kernels.
Can someone highlight general approaches or methods for proving that a given function is NOT a valid kernel function?
If both of the above approaches fail, what else should one try and how does one conclude that the given function is not a valid kernel function?