Displaying similar documents to “Concerning the envelope of holomorphy of a compact differentiable submanifold of a complex manifold”

Linear Kierst-Szpilrajn theorems

L. Bernal-González (2005)

Studia Mathematica

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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...