We prove the following result which extends in a somewhat "linear" sense a theorem by Kierst and Szpilrajn and which holds on many "natural" spaces of holomorphic functions in the open unit disk 𝔻: There exist a dense linear manifold and a closed infinite-dimensional linear manifold of holomorphic functions in 𝔻 whose domain of holomorphy is 𝔻 except for the null function. The existence of a dense linear manifold of noncontinuable functions is also shown in any domain for its full space of holomorphic functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-4,
author = {L. Bernal-Gonz\'alez},
title = {Linear Kierst-Szpilrajn theorems},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {55-69},
zbl = {1062.30003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-4}
}
L. Bernal-González. Linear Kierst-Szpilrajn theorems. Studia Mathematica, Tome 166 (2005) pp. 55-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-4/