## 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)

### MSC:

 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
Full Text:

### References:

 [1] Sato, M.), Kawai, T.) et Kashiwara, M.) .- Hyperfunctions and Pseudo differential equations, , 287 (1973). · Zbl 0277.46039 [2] Kaneko, A.) .- Remarks on hyperfunctions with analytic parameters, J. Fac. Sc. Univ. Tokyo Sec. 1A, 22 (1975) pp. 371-407; II ibid., 25 (1978) pp. 67-73. · Zbl 0381.46025 [3] Kaneko, A.) .- On hyperfunctions with analytic parameters, Academic Press, Inc. Algebraic Analysis, vol. I (1988) pp. 267-276. · Zbl 0682.32004 [4] Marti, J.-A.) .- Sur la rigidité comparée de fonctions, distributions ou hyperfonctions analytiques par rapport à un groupe de variables, Pacific Journal of Math., 150, n° 2 (1991) pp. 359-382. · Zbl 0693.32002 [5] Hörmander, L.) .- The Analysis of Linear Partial Differential Operators I, Springer-Verlag (1983). · Zbl 0521.35002 [6] Boman, J.) .- A local Vanishing Theorem for Distributions, Reports Department of Math. Univ. Stockholm, ISSN 0348-7652, n° 3 (1991). · Zbl 0785.46039
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.