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Lacunary series in Q K spaces

Hasi Wulan, Kehe Zhu (2007)

Studia Mathematica

Under mild conditions on the weight function K we characterize lacunary series in the so-called K spaces.

Linear Kierst-Szpilrajn theorems

L. Bernal-González (2005)

Studia Mathematica

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...

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