Abstract
It is shown that a nuclear Fréchet spaceE has the property (DN) if and only if every holomorphic function onE *, the strongly dual space ofE, with values in the strongly dual space of a Fréchet spaceF having the property (\(\bar \Omega\)) can be represented in the exponential form. Moreover, it is shown that the space of holomorphic functions onC ∞, the space of all complex number sequences, has a linearly absolutely exponential representation system. But the space of holomorphic functions onE * does not have such a system whenE is a nuclear Fréchet space that does not have the property (DN).
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Supported by the State Program for Fundamental Researches in Natural Sciences
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Nguyen Minh Ha, Nguyen Van Khue The property (DN) and the exponential representation of holomorphic functions. Monatshefte für Mathematik 120, 281–288 (1995). https://doi.org/10.1007/BF01294861
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DOI: https://doi.org/10.1007/BF01294861