I'm convinced that there is no such a mathematician whose name is "kernel". The wiki article about kernel doesn't include history in its content.
So I wonder, who is the first mathematician to use kernel in his work and on which paper.
See the entry for kernel in Jeff Miller's Earliest Known Uses of Some of the Words of Mathematics web pages.
By the way, not mentioned in Jeff Miller's web pages is the "perfect kernel" in the Cantor-Bendixson theorem sense ("nucleus" and "core" are alternative terms that are also used). My initial thought was that this may predate most or all of the other uses at Jeff Miller's web pages, but after looking through some of my references on the Cantor-Bendixson theorem, I believe "kernel" was not used in this way until 1914 1st edition of Hausdorff's Grundzüge der Mengenlehre. See pp. 220 & 226 in this copy of Hausdorff's 1914 book, where "Kern" -- the German version of the word -- is used.