// BTW kernels can be characterised a being univeral, characteristic, translation-invariant, strictly positive-definite, What's that?
Stricly positive kernels on [$]\Omega[$] are functions [$]k(x,y)[$] satisfying [$]k(x^i,x^j)_{i,j \le N}[$] is a s.d.p matrix for any set of distinct points [$]x^i \in \Omega[$]
Translation invariant kernels are kernels having form [$]k(x,y) = \varphi(x-y)[$]
I found some definitions of Universal kernels in
https://arxiv.org/pdf/1003.0887.pdf. To me it might be a little bit obsolete definition, telling you that a kernel can reproduce any continuous function in some Banach space.
I found the definition of characteristic kernels in this reference :
https://www.ism.ac.jp/~fukumizu/papers/fukumizu_etal_nips2007_extended.pdf. To me it is a little bit strange definition. As far as I understood : consider a kernel [$]k(x,y)[$], generating a space of functions [$]H_k[$]. It is said characteristic if for any two probability measure [$]\mu, \nu[$], if [$]\int f(x) d\mu = \int f(x) d\nu[$] for any [$]f \in H_k[$] implies [$]\mu = \nu[$]. I would say that both definition (characteristic and universal kernels) are almost surely equivalent