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Analyticité partielle et suites d’unicité. (Partial analyticity and uniqueness sequences). (French) Zbl 0762.32002
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 J. Boman [C. R. Acad. Sci., Paris, Sér. I 315, 1231-1234 (1992)].
Reviewer: A.Kaneko (Komaba)
MSC:
32A10 Holomorphic functions of several complex variables
32A45 Hyperfunctions
46F15 Hyperfunctions, analytic functionals
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