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One meaning of the word kernel is the set of $u$ so that $T(u)=0$. Another meaning of the word kernel is the "kernel" of an integral transform. Is there any relationship between these two?

In addition, the word "kernel" is used to refer to the kernels of group homomorphisms. Here, a discussion has concluded that group kernels came before and are distinct from linear map kernels. This leaves integral transform kernels, which might be the same as one or the other in some way that is not clear to me, or could also be a third distinct thing with the same name.

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There is no relation, except that both come from the German word "Kern" which is usually translated as "nucleus" but has very many meanings in German (see Google translate).

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