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

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Snježana Maksimović, Svetlana Mincheva-Kamińska, Stevan Pilipović, Petar Sokoloski

Faculty 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, Macedonia

Abstract: We introduce and investigate two types of the space 𝒰 * of s-ultradistributions meant as equivalence classes of suitably defined fundamental sequences of smooth functions; we prove the existence of an isomorphism between 𝒰 * and the respective space 𝒟 '* of ultradistributions: of Beurling type if *=(p! t ) and of Roumieu type if *={p! t }. We also study the spaces 𝒯 * and 𝒯 ˜ * of t-ultradistributions and t ˜-ultradistributions, respectively, and show that these spaces are isomorphic with the space 𝒮 '* of tempered ultradistributions both in the Beurling and the Roumieu case.

Keywords: fundamental sequences, Hermite expansions

Classification (MSC2000): 46F05; 46F10

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Electronic fulltext finalized on: 8 Nov 2016. This page was last modified: 14 Nov 2016.

© 2016 Mathematical Institute of the Serbian Academy of Science and Arts
© 2016 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition