Analytic continuation of generalized functions. (English) Zbl 0662.46047
The following result is proved:
Let \(\Omega\) be a connected open non void set in \(C^ n\) and let F be a generalized holomorphic function on \(\Omega\) ; if F is null on a non void open subset of \(\Omega\), then F is null in \(\Omega\).
The result was announced in J. F. Colombeau: Elementary introduction to new generalized functions, North-Holland Math. Studies, No.113 (1985; Zbl 0584.46024), where a sketch of the proof in the case \(n=1\) was given.
Let \(\Omega\) be a connected open non void set in \(C^ n\) and let F be a generalized holomorphic function on \(\Omega\) ; if F is null on a non void open subset of \(\Omega\), then F is null in \(\Omega\).
The result was announced in J. F. Colombeau: Elementary introduction to new generalized functions, North-Holland Math. Studies, No.113 (1985; Zbl 0584.46024), where a sketch of the proof in the case \(n=1\) was given.
Reviewer: I.Cioranescu
MSC:
| 46F10 | Operations with distributions and generalized functions |
Citations:
Zbl 0584.46024References:
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