Displaying similar documents to “Structure theorem for functionals in the space 𝔖 ω 1 , ω 2 ' .”

Generalized Hermitean ultradistributions

C. Andrade, L. Loura (2009)

Mathematica Bohemica

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In this paper we define, by duality methods, a space of ultradistributions ω ' ( ℝ N ) . This space contains all tempered distributions and is closed under derivatives, complex translations and Fourier transform. Moreover, it contains some multipole series and all entire functions of order less than two. The method used to construct 𝔾 ω ' ( ℝ N ) led us to a detailed study, presented at the beginning of the paper, of the duals of infinite dimensional locally convex spaces that are inductive limits of finite...

On a space of smooth functions on a convex unbounded set in ℝn admitting holomorphic extension in ℂn

Il’dar Musin, Polina Yakovleva (2012)

Open Mathematics

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For some given logarithmically convex sequence M of positive numbers we construct a subspace of the space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in ℝn. Due to the conditions on M each function of this space admits a holomorphic extension in ℂn. In the current article, the space of holomorphic extensions is considered and Paley-Wiener type theorems are established. To prove these theorems, some auxiliary results on extensions of holomorphic...