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Linear structure of weighted holomorphic non-extendibility
Published online by Cambridge University Press: 17 April 2009
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In this paper, it is proved that, for any domain G of the complex plane, there exists 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 f of M1 or M2 and, in addition, the growth of f near each boundary point is as fast as prescribed.
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- Copyright © Australian Mathematical Society 2006
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