Linear Kierst–Szpilrajn theorems

L. Bernal-González ¹

¹ Departamento de Análisis Matemático Facultad de Matemáticas, Apdo. 1160 Avda. Reina Mercedes 41080 Sevilla, Spain

Studia Mathematica, Tome 166 (2005) no. 1, pp. 55-69

Résumé

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 ${\mathbb D}$: There exist a dense linear manifold and a closed infinite-dimensional linear manifold of holomorphic functions in ${\mathbb D}$ whose domain of holomorphy is ${\mathbb D}$ 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.

Détail

DOI : 10.4064/sm166-1-4

Mots-clés : prove following result which extends somewhat linear sense theorem kierst szpilrajn which holds many natural spaces holomorphic functions unit disk mathbb there exist dense linear manifold closed infinite dimensional linear manifold holomorphic functions mathbb whose domain holomorphy mathbb except null function existence dense linear manifold noncontinuable functions shown domain its full space holomorphic functions