Linear Kierst-Szpilrajn theorems

@article{L2005,
abstract = {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.},
author = {L. Bernal-González},
journal = {Studia Mathematica},
keywords = {linear manifold; analytic continuation},
language = {eng},
number = {1},
pages = {55-69},
title = {Linear Kierst-Szpilrajn theorems},
url = {http://eudml.org/doc/285182},
volume = {166},
year = {2005},
}

TY - JOUR
AU - L. Bernal-González
TI - Linear Kierst-Szpilrajn theorems
JO - Studia Mathematica
PY - 2005
VL - 166
IS - 1
SP - 55
EP - 69
AB - 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.
LA - eng
KW - linear manifold; analytic continuation
UR - http://eudml.org/doc/285182
ER -