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)

Risultato della ricerca: Other contribution

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).
Lingua originaleEnglish
Numero di pagine1
Stato di pubblicazionePublished - 2017

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Ultradistributions
Equivalence class
t-distribution
D-space
Test function
Open set
Smooth function
Isomorphism
Operator

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@misc{88c0d6ab823e4e358db71a52b8178356,
title = "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).",
author = "Francesco Tschinke",
year = "2017",
language = "English",
type = "Other",

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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

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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

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M3 - Other contribution

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