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Linear structure of weighted holomorphic non-extendibility

Published online by Cambridge University Press:  17 April 2009

L. Bernal-González
L. Bernal-González
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Apdo. 1160, Avda. Reina Mercedes, 41080 Sevilla, Spain, e-mail: lbernal@us.es
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 3 , June 2006 , pp. 335 - 344
Copyright
Copyright © Australian Mathematical Society 2006

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