Linear Kierst-Szpilrajn theorems

• Autorzy: L. Bernal-González
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 30H05: Bounded analytic functions
• 30B10: Power series (including lacunary series)
• 30D40: Cluster sets, prime ends, boundary behavior
• 30B30: Boundary behavior of power series, over-convergence

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 166
• Numer: 1
• Strony: 55-69

Daty

wydano

2005

Twórcy

autor

L. Bernal-González

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

Identyfikatory

DOI

10.4064/sm166-1-4