no. 1
The general complex case of the Bernstein-Nachbin approximation problem
Annales de l'Institut Fourier, Tome 28 (1978) no. 1, pp. 193-206.

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.

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.

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     title = {The general complex case of the {Bernstein-Nachbin} approximation problem},
     journal = {Annales de l'Institut Fourier},
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Machado, S.; Prolla, Joao Bosco. The general complex case of the Bernstein-Nachbin approximation problem. Annales de l'Institut Fourier, Tome 28 (1978) no. 1, pp. 193-206. doi : 10.5802/aif.685. https://aif.centre-mersenne.org/articles/10.5802/aif.685/

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