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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.

Danu
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albo
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    See the entry for kernel here. By the way, I'm nearly certain that "kernel" was used (for the "perfect kernel" that occurs in the Cantor-Bendixson theorem) earlier than any of the present entries. I'll look at some of my references at home and send the information to Jeff if I'm able to verify this. – Dave L Renfro May 11 '16 at 16:33
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    This is answered under What came first? The kernel from vector spaces or from group theory? http://hsm.stackexchange.com/questions/2149/what-came-first-the-kernel-from-vector-spaces-or-from-group-theory/2155#2155 – Conifold May 12 '16 at 07:49
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    It seems that "kernel" (via the German "Kern") for the perfect set that the Cantor-Bendixson theorem gives you first appeared in the 1914 1st edition of Hausdorff's Grundzüge der Mengenlehre, so I guess this might not be worth including. I thought William H. Young, Hardy, Hobson, Hedrick, Frechet, Vivanti, or some others writing about the CB theorem earlier than this used "kernel", but that seems not to be the case ("nucleus" and "core" were used, but not "kernel"). – Dave L Renfro May 12 '16 at 17:38
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    Possible duplicate of What came first? The kernel from vector spaces or from group theory? – Francois Ziegler Jun 06 '18 at 11:32

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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.

Dave L Renfro
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