*(English)*Zbl 0657.35018

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.

##### MSC:

35B60 | Continuation of solutions of PDE |

32D20 | Removable singularities (several complex variables) |

35N05 | Overdetermined systems of PDE with constant coefficients |

35-02 | Research monographs (partial differential equations) |

32-02 | Research monographs (several complex variables) |