Hartogs's extension theorem: Difference between revisions

Revision as of 10:51, 10 July 2021

Revision as of 10:53, 10 July 2021

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'''Theorem''' {{harvtxt|Hartogs|1906}}: any holomorphic functions <math>f</math> on <math>H_\varepsilon</math> are analytically continued to <math>\Delta^2</math> . Namely, there is a holomorphic function <math>F</math> on <math>\Delta^2</math> such that <math>F=f</math> on <math>H_\varepsilon</math> .

Such a phenomenon is called '''Hartogs's phenomenon''', which lead to the notion of this Hartogs's extension theorem and the [[___domain of holomorphy]]. Such phenomena never happen in the case of one variable.

==Formal statement==