Abstract
Let H(Q) be the space of all the functions which are holomorphic on an open neighbourhood of a convex locally closed subset Q of \(\mathbb C^N\), endowed with its natural projective topology. We characterize when the countable weighted inductive limit of Fréchet spaces which is obtained as the Fourier Laplace transform of the dual \(H(Q)'\) of H(Q) coincides algebraically with its projective hull.
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Acknowledgments
I would like to express my gratitude to Professor J. Bonet and Professor R. Meise for their interest in this research, for fruitful discussions.
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Melikhov, S.N. Algebraic projective descriptions and the Fantappiè transformation. RACSAM 110, 573–583 (2016). https://doi.org/10.1007/s13398-015-0250-6
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DOI: https://doi.org/10.1007/s13398-015-0250-6
Keywords
- Projective description
- Weighted (LF)-space of entire functions
- Locally closed convex set
- Fantappiè transformation