Remarks on uniqueness sequences and partial analyticity. (Remarques sur les suites d’unicité et l’analyticité partielle.) (French) Zbl 0777.32002

The author extends his results on the study of uniqueness introduced in Pac. J. Math. 150, 359-382 (1991; Zbl 0693.32002) for analytic functions or distributions with analytic parameters. A sequence \(z_ k\) of \(\mathbb{C}^ k\) is called a weak \(\rho\)-uniqueness sequence if it satisfies some density conditions with respect to a family of mappings \(\rho=(\rho_ \varepsilon):\mathbb{N}^ n\to\mathbb{R}^*_ +\), which is here allowed to be more general than in the former work. Uniqueness results of the type: \(f^{(k)}z_ k=0\) for all \(k\) imply \(f\equiv 0\) and analogous ones concerning analytic parameters are generalized in accordance with this notion. Some open problems in relation to J. Boman’s recent work are proposed.
Reviewer: A.Kaneko (Komaba)


32A22 Nevanlinna theory; growth estimates; other inequalities of several complex variables
32A45 Hyperfunctions
30B40 Analytic continuation of functions of one complex variable
46F99 Distributions, generalized functions, distribution spaces


Zbl 0693.32002
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