Publications de l’Institut Mathématique, Nouvelle Série Vol. 100[114], No. 1/1, pp. 17–48 (2016) 

A SEQUENTIAL APPROACH TO ULTRADISTRIBUTION SPACESSnježana Maksimović, Svetlana MinchevaKamińska, Stevan Pilipović, Petar SokoloskiFaculty of Electrical Engineering, University of Banja Luka, Banja Luka, Bosnia and Herzegovina; Faculty of Mathematics and Natural Sciences University of Rzeszow, Rzeszow, Poland; Faculty of Sciences and Mathematics, University of Novi Sad, Novi Sad, Serbia; Faculty of Mathematics and Natural Sciences, University of Sts. Cyril and Methodius, Skopje, MacedoniaAbstract: We introduce and investigate two types of the space ${\mathcal{U}}^{*}$ of $s$ultradistributions 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 ${\mathcal{D}}^{\text{'}*}$ of ultradistributions: of Beurling type if $*=\left(p{!}^{t}\right)$ and of Roumieu type if $*=\left\{p{!}^{t}\right\}$. 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 ${\mathcal{S}}^{\text{'}*}$ of tempered ultradistributions both in the Beurling and the Roumieu case. Keywords: fundamental sequences, Hermite expansions Classification (MSC2000): 46F05; 46F10 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 8 Nov 2016. This page was last modified: 14 Nov 2016.
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