an:00168578
Zbl 0777.32002
Marti, Jean-Andr??
Remarks on uniqueness sequences and partial analyticity
FR
Ann. Fac. Sci. Toulouse, VI. S??r., Math. 1, No. 1, 43-52 (1992).
00009559
1992
j
32A22 32A45 30B40 46F99
unique continuation property; uniqueness; analytic functions; distributions with analytic parameters
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.
A.Kaneko (Komaba)
Zbl 0693.32002