The general complex case of the Bernstein-Nachbin approximation problem
Annales de l'Institut Fourier, Volume 28 (1978) no. 1, p. 193-206
We present a solution to the (strict) Bernstein-Nachbin approximation problem in the general complex case. As a corollary, we get proofs of the analytic, the quasi-analytic, and the bounded criteria for localizability in the general complex case. This generalizes the known results of the real or self-adjoint complex cases, in the same way that Bishop’s Theorem generalizes the Weierstrass-Stone Theorem. However, even in the real or self-adjoint complex cases, the results that we obtain are stronger than the previously known results of the literature.
On présente ici une solution du problème d’approximation de Bernstein-Nachbin dans le cas complexe général, c’est-à-dire non nécessairement auto-adjointe. On généralise ainsi les résultats connus de cette théorie de la même façon que le théorème d’approximation de Bishop généralise le théorème de Weierstrass-Stone.
@article{AIF_1978__28_1_193_0,
     author = {Machado, S. and Prolla, Joao Bosco},
     title = {The general complex case of the Bernstein-Nachbin approximation problem},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {28},
     number = {1},
     year = {1978},
     pages = {193-206},
     doi = {10.5802/aif.685},
     mrnumber = {81g:46069},
     zbl = {0365.41007},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_1978__28_1_193_0}
}
The general complex case of the Bernstein-Nachbin approximation problem. Annales de l'Institut Fourier, Volume 28 (1978) no. 1, pp. 193-206. doi : 10.5802/aif.685. https://aif.centre-mersenne.org/item/AIF_1978__28_1_193_0/

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