Spaces of Ultradistributions of Beurling Type Over $\boldsymbol{\mathbb{R}^d_+}$ Through Laguerre Expansions
DOI:
https://doi.org/10.5644/SJM.12.3.11Keywords:
Spaces of ultradistributions of Beurling type over $\mathbb{R}^d_ $, Laguerre series expansions, Schwartz kernel theoremAbstract
In this paper we define the spaces of ultradistributions of Beurling type over $\mathbb{R}^d_+$ and their dual spaces. Characterization of the spaces is given by the Laguerre series expansions and the growth rate of the corresponding Fourier-Laguerre coefficients. As a consequence of these characterizations, we obtain a deep insight into their topological structure and we prove the Schwartz kernel theorems.
* This paper was presented at the International Scientific Conference Graded structures in algebra and their applications, dedicated to the memory of Prof. Marc Krasner, IUCDubrovnik, Cratia, September, 22-24, 2016.
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