MR3586679 Reviewed Maksimović, Snježana(BS-BALUEL); Mincheva-Kamińska, Svetlana(PL-RZSZM); Pilipović, Stevan(SE-NOVIS-NDM); Sokoloski, Petar(MK-SKOPN-NDM) A sequential approach to ultradistribution spaces. (English summary) Publ. Inst. Math. (Beograd) (N.S.) 100(114) (2016), 17–48. 46F05 (46F10)

Abstract

The purpose of the paper is to investigate ultradistributions of both Beurling and Roumieu (briefly, B and R) types with the help of a sequential approach, considering certain equivalence classes of fundamental sequences of smooth functions defined by ultradifferential operators. More precisely, the authors define as s-ultradistributions the equivalence classes U(t) and U{t} of B and R types respectively on test functions belonging respectively to D′(t)(Ω) and D′{t}(Ω) on the open set Ω⊂Rn, and T(t), T{t}, T~(t) and T~{t} of (tempered) t- and t~-distributions, and study their properties. Finally, the authors prove the existence of topological isomorphism between the classes T(t), T{t}, T~(t), T~{t} and the spaces of tempered ultradistributions of B and R types, and between U(t), U{t} and the respective spaces D′(t)(Ω), D′{t}(Ω).