Spaces of Ultradistributions of Beurling Type Over Rᵈ₊ Through Laguerre Expansions

In this paper we define the spaces of ultradistributions of Beurling type over Rᵈ₊ 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.