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Ultradistributions of Roumieu type and projective descriptions. (English) Zbl 0978.46020

Let \(\text{WH}(\mathbb{C}^N)\) be the weighted inductive limit of Fréchet spaces of entire functions which is obtained as the Fourier-Laplace transform of the space of ultradistributions with compact support of Roumieu type (as defined by Braun-Meise-Taylor); the main result states that \(\text{WH}(\mathbb{C}^N)\) coincides algebraically with its projective hull but not topologically, i.e., the topological projective description of Bierstedt-Meise-Summers fails in this situation. In the case of the space \(\text{WC}(\mathbb{C}^N)\) obtained by replacing holomorphic functions by continuous ones in the definition of \(\text{WH}(\mathbb{C}^N)\) it is known that the topological projective description works but it is proved here that it is a proper subspace of its projective hull.

MSC:

46F05 Topological linear spaces of test functions, distributions and ultradistributions
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