# How is the word kernel associated with distributions?

I am trying to rationalize the meaning of the term kernel, especially when it is associated with distributions. The English and German etymology all show that the literal meaning is corn (English) and grain (in German). For example the term Gaussian kernel is often used in digital filtering to remove noise from signal. According to the Earliest Known Uses of Math Words website kernel entered statistics with the use of Fourier theory in describing estimates for spectral density and probability density functions. However it does not explain the choice.

What is the rationalization behind the choice of this word, I mean what is common in the original meaning of kernel and window functions as shown on Wikipedia? The term window function makes much more sense.

• @M.Farooq Keep in mind that this is just my guess, Fredholm does not say anything. In an integral equation you have a term $\int K(x,y)f(y)\,dy$, with $K$ tucked inside, like a core, and it stays the same for all solutions $f$. – Conifold Apr 29 at 21:05