an:00098110
Zbl 0762.32002
Marti, Jean-Andr??
Analyticit?? partielle et suites d'unicit??. (Partial analyticity and uniqueness sequences)
FR
C. R. Acad. Sci., Paris, S??r. I 314, No. 11, 789-792 (1992).
00008103
1992
j
32A10 32A45 46F15
uniqueness theorem for holomorphic functions; uniqueness sequence; hyperfunctions; real analytic parameters
The author introduces two kinds of uniqueness sequences \((z_ k)\), weak and strong, for a family of mappings \(\rho=(\rho_ \varepsilon)\), \(\varepsilon=(\varepsilon_ 1,\dots,\varepsilon_ n)\) being positive parameters, which describes the density of this sequence. Employing this, he generalizes the uniqueness theorem for holomorphic functions in the form that if \((z_ k)\) is a weak uniqueness sequence, \(f^{(k)}(z_ k)=0\) for all \(k\) implies \(f\equiv 0\). He also gives an analogy of this uniqueness theorem for hyperfunctions with compact support containing real analytic parameters \(t\) with respect to a strong uniqueness sequence \((t_ k)\). Some open problems for the case of distributions with real analytic parameters but without restriction of support are discussed. These may be progressed in view of a recent result of \textit{J. Boman} [C. R. Acad. Sci., Paris, S??r. I 315, 1231-1234 (1992)].
A.Kaneko (Komaba)