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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},
pages = {193--206},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {28},
number = {1},
year = {1978},
doi = {10.5802/aif.685},
mrnumber = {81g:46069},
zbl = {0365.41007},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/aif.685/}
}
TY - JOUR AU - Machado, S. AU - Prolla, Joao Bosco TI - The general complex case of the Bernstein-Nachbin approximation problem JO - Annales de l'Institut Fourier PY - 1978 SP - 193 EP - 206 VL - 28 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://geodesic.mathdoc.fr/articles/10.5802/aif.685/ DO - 10.5802/aif.685 LA - en ID - AIF_1978__28_1_193_0 ER -
%0 Journal Article %A Machado, S. %A Prolla, Joao Bosco %T The general complex case of the Bernstein-Nachbin approximation problem %J Annales de l'Institut Fourier %D 1978 %P 193-206 %V 28 %N 1 %I Institut Fourier %C Grenoble %U http://geodesic.mathdoc.fr/articles/10.5802/aif.685/ %R 10.5802/aif.685 %G en %F AIF_1978__28_1_193_0
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
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