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Zbl 0657.35018
Struppa, Daniele C.
The first eighty years of Hartogs' theorem. (English)
[J] Semin. Geom., Univ. Studi Bologna 1987-1988, 127-211 (1988).

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. \par 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. \par The seminar notes including this article seem to be available on request to the University of Bologna.
[A.Kaneko]

MSC 2000:: *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)

Keywords: survey; extension of solutions; systems of convolution equations; Hartogs continuity theory; holomorphic functions; compact singularity; Ehrenpreis' approach; overdetermined systems; hyperfunction theory; equations of infinite order

Cited in: Zbl 0675.32011

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