Geodesic
A Sequential Approach to Ultradistribution Spaces
Publications de l'Institut Mathématique, _N_S_100 (2016) no. 114, p. 17

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We introduce and investigate two types of the space $\mathcal{U}^*$ of $s$-ultra\-distri\-butions meant as equivalence classes of suitably defined fundamental sequences of smooth functions; we prove the existence of an isomorphism between $\mathcal{U}^*$ and the respective space $\mathcal{D}'^*$ of ultradistributions: of Beurling type if $*=(p!^t)$ and of Roumieu type if $*=\{p!^t\}$. We also study the spaces $\mathcal{T}^*$ and $\tilde{\mathcal{T}}^*$ of $t$-ultradistributions and $\tilde t$-ultradistributions, respectively, and show that these spaces are isomorphic with the space $\mathcal{S}'^*$ of tempered ultradistributions both in the Beurling and the Roumieu case.
DOI : 10.2298/PIM1614017M
Classification : 46F05 46F10
Keywords: fundamental sequences, Hermite expansions 
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     title = {A {Sequential} {Approach} to {Ultradistribution} {Spaces}},
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Snježana Maksimović; Svetlana Mincheva-Kamińska; Stevan Pilipović; Petar Sokoloski. A Sequential Approach to Ultradistribution Spaces. Publications de l'Institut Mathématique, _N_S_100 (2016) no. 114, p. 17 . doi: 10.2298/PIM1614017M

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