TY - GEN

T1 - 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)

AU - Tschinke, Francesco

PY - 2017

Y1 - 2017

N2 - 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).

AB - 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).

UR - http://hdl.handle.net/10447/325759

UR - https://mathscinet.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=RVCN&pg5=TI&pg6=RVCN&pg7=ALLF&pg8=ET&review_format=html&s4=tschinke&s5=&s6=&s7=&s8=All&sort=Newest&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=6&mx-pid=3586679

M3 - Other contribution

ER -