We show that the converse of the aproximation theorem of Andreotti and Grauert does not hold. More precisely we construct a -complete open subset (which is an analytic complement in the unit ball) such that the restriction map has a dense image for every but the pair is not a -Runge pair.
@article{ASNSP_2003_5_2_2_231_0,
author = {Col\c{t}oiu, Mihnea},
title = {On $q${-Runge} pairs},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {231--235},
year = {2003},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 2},
number = {2},
mrnumber = {2004963},
zbl = {1170.32308},
language = {en},
url = {https://www.numdam.org/item/ASNSP_2003_5_2_2_231_0/}
}
Colţoiu, Mihnea. On $q$-Runge pairs. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 2, pp. 231-235. https://www.numdam.org/item/ASNSP_2003_5_2_2_231_0/
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