This is an enlarged version, added with the historical survey, of the author’s lecture on the extension of solutions of systems of convolution equations. Chap. 1 starts with the original Hartogs continuity theory on the extension of holomorphic functions of several variables to compact singularity, and then surveys its early generalizations or re-proofs by Severi, Fubini, Segre, Martinelli. Chap. 2 introduces Ehrenpreis’ approach from the viewpoint of overdetermined systems which was epoch making in this problem. Chap. 3 surveys hyperfunction theory and its contribution to this problem. Chap. 4 treats the author’s original work on the extension of solutions of systems of convolution equations, including systems of differential equations of infinite order as a particular case.
As a whole this is a good survey to the problem of extension of solutions of Hartogs type, although a little more references (especially, contributions of some Russians) should be added in order to be a complete survey including the case of isolated singularity, or the case of non- compact singularity.
The seminar notes including this article seem to be available on request to the University of Bologna.