Abstract
Using the Berezin transformation, we give a multidimensional analog of a uniqueness theorem of Nikolskii concerning distance functions and subspaces of a Hilbert space of analytic functions. Then, we establish some uniqueness properties connecting two analytic X-valued functions F and G that satisfy ‖F(z)‖≡‖G(z)‖ for all z∈Ω, where X is a Banach space and Ω is a connected domain in {\(\mathbb{C}^n \)}. The particular case where {\(\mathop {X = \ell }\nolimits_n^p \)} and {\(\Omega = \left\{ {z \in \mathbb{C}:\left| z \right|< 1} \right\}\)} will lead us to the notion of flexible and inflexible functions. We give a complete description of these functions for p=+∞, {\(n \in \mathbb{N}^ * \)}, and for n=2, 1≤p≤+∞. Bibliography: 19 titles.
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 242–267.
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Fricain, E. Uniqueness theorems for analytic vector-valued functions. J Math Sci 101, 3193–3210 (2000). https://doi.org/10.1007/BF02673744
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DOI: https://doi.org/10.1007/BF02673744