Linear structure of the weighted holomorphic non-extendibility

Description

In this paper, it is proved that, for any domain G of the complex plane, there exist an infinite-dimensional closed linear submanifold M1 and a dense linear submanifold M2 with maximal algebraic dimension in the space H(G) of holomorphic functions on G such that G is the domain of holomorphy of every nonzero member of f of M1 or M2 and, in addition, the growth of f near each boundary point is as fast as prescribed.

Abstract

Plan Andaluz de Investigación (Junta de Andalucía)

Abstract

Dirección General de Enseñanza Superior (DGES). España

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