Completing the Valdivia–Vogt tables of sequence-space representations of spaces of smooth functions and distributions
In the Valdivia–Vogt structure tables presented in Ortner and Wagner (J Math Anal Appl 404(1):1–10, 2013 ) there are two gaps. We fill in these gaps by proving the representations D F ≅ s ⊗ ^ π C ( N ) and B ˙ ′ ≅ s ′ ⊗ ^ c 0 , where D F is a pre-dual space of the space of distributions of finite or...
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| Vydané v: | Monatshefte für Mathematik Ročník 177; číslo 1; s. 1 - 14 |
|---|---|
| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Vienna
Springer Vienna
01.05.2015
|
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| ISSN: | 0026-9255, 1436-5081 |
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| Abstract | In the Valdivia–Vogt structure tables presented in Ortner and Wagner (J Math Anal Appl 404(1):1–10,
2013
) there are two gaps. We fill in these gaps by proving the representations
D
F
≅
s
⊗
^
π
C
(
N
)
and
B
˙
′
≅
s
′
⊗
^
c
0
, where
D
F
is a pre-dual space of the space of distributions of finite order introduced by J. Horváth and the space
B
˙
′
is the space of distributions vanishing at infinity introduced by L. Schwartz. |
|---|---|
| AbstractList | In the Valdivia–Vogt structure tables presented in Ortner and Wagner (J Math Anal Appl 404(1):1–10,
2013
) there are two gaps. We fill in these gaps by proving the representations
D
F
≅
s
⊗
^
π
C
(
N
)
and
B
˙
′
≅
s
′
⊗
^
c
0
, where
D
F
is a pre-dual space of the space of distributions of finite order introduced by J. Horváth and the space
B
˙
′
is the space of distributions vanishing at infinity introduced by L. Schwartz. |
| Author | Bargetz, Christian |
| Author_xml | – sequence: 1 givenname: Christian surname: Bargetz fullname: Bargetz, Christian email: christian.bargetz@uibk.ac.at organization: Institut für Mathematik, Universität Innsbruck |
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| Cites_doi | 10.1007/978-3-322-90559-8 10.1007/s00013-012-0373-3 10.1007/BF01219081 10.1002/mana.201200258 10.5802/aif.77 10.1007/BFb0070913 10.1201/9781003072577-18 10.1007/978-3-642-61715-7 10.1090/memo/0016 10.1007/BF02787718 10.1016/j.jmaa.2013.02.041 10.1007/978-1-4612-1468-7 10.4064/dm495-0-1 10.1007/BFb0097765 |
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| Keywords | Distributions of finite order Distributions vanishing at infinity Sequence-space representation 46E10 46A45 46F05 |
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| References | Robertson, Robertson (CR13) 1964 Valdivia (CR22) 1981; 177 CR2 CR4 Valdivia (CR20) 1980; 320 CR6 Bargetz (CR1) 2012; 98 CR19 CR7 CR17 Bargetz (CR5) 2014; 287 CR9 CR15 Jarchow (CR11) 1981 CR14 CR24 CR12 CR10 CR21 Schwartz (CR16) 1958; 8 Bargetz (CR3) 2013 Valdivia (CR23) 1982 Seely (CR18) 1964; 15 Frerick (CR8) 2007; 602 650_CR2 C Bargetz (650_CR3) 2013 650_CR4 650_CR6 C Bargetz (650_CR5) 2014; 287 650_CR19 650_CR7 H Jarchow (650_CR11) 1981 650_CR14 650_CR9 650_CR15 650_CR17 650_CR10 650_CR21 C Bargetz (650_CR1) 2012; 98 650_CR12 M Valdivia (650_CR23) 1982 650_CR24 L Schwartz (650_CR16) 1958; 8 M Valdivia (650_CR22) 1981; 177 L Frerick (650_CR8) 2007; 602 AP Robertson (650_CR13) 1964 RT Seely (650_CR18) 1964; 15 M Valdivia (650_CR20) 1980; 320 |
| References_xml | – ident: CR21 – ident: CR19 – year: 1982 ident: CR23 publication-title: Topics in Locally Convex Spaces, North-Holland Mathematics Studies – volume: 15 start-page: 625 year: 1964 end-page: 626 ident: CR18 article-title: Extension of functions defined in a half space publication-title: Proc. Am. Math. Soc. – volume: 320 start-page: 97 year: 1980 end-page: 98 ident: CR20 article-title: A representation of the space publication-title: J. Reine Angew. Math. – ident: CR4 – ident: CR14 – ident: CR15 – ident: CR2 – ident: CR12 – ident: CR17 – ident: CR10 – ident: CR9 – year: 1981 ident: CR11 publication-title: Locally Convex Spaces doi: 10.1007/978-3-322-90559-8 – volume: 98 start-page: 317 issue: 4 year: 2012 end-page: 326 ident: CR1 article-title: A sequence space representation of L. Schwartz’ space publication-title: Arch. Math. (Basel) doi: 10.1007/s00013-012-0373-3 – year: 2013 ident: CR3 publication-title: Explicit Representations of Spaces of Smooth Functions and Distributions – ident: CR6 – volume: 177 start-page: 463 issue: 4 year: 1981 end-page: 478 ident: CR22 article-title: A representation of the space publication-title: Math. Z. doi: 10.1007/BF01219081 – volume: 287 start-page: 10 issue: 1 year: 2014 end-page: 22 ident: CR5 article-title: Commutativity of the Valdivia–Vogt table of representations of function spaces publication-title: Math. Nachr. doi: 10.1002/mana.201200258 – ident: CR7 – year: 1964 ident: CR13 publication-title: Topological Vector Spaces. Cambridge Tracts in Mathematics and Mathematical Physics – ident: CR24 – volume: 602 start-page: 123 year: 2007 end-page: 154 ident: CR8 article-title: Extension operators for spaces of infinite differentiable Whitney jets publication-title: J. Reine Angew. Math. – volume: 8 start-page: 1 year: 1958 end-page: 209 ident: CR16 article-title: Théorie des distributions à valeurs vectorielles. II publication-title: Ann. Inst. Fourier. Grenoble doi: 10.5802/aif.77 – volume: 15 start-page: 625 year: 1964 ident: 650_CR18 publication-title: Proc. Am. Math. Soc. – volume: 8 start-page: 1 year: 1958 ident: 650_CR16 publication-title: Ann. Inst. Fourier. Grenoble doi: 10.5802/aif.77 – volume: 98 start-page: 317 issue: 4 year: 2012 ident: 650_CR1 publication-title: Arch. Math. (Basel) doi: 10.1007/s00013-012-0373-3 – volume-title: Topics in Locally Convex Spaces, North-Holland Mathematics Studies year: 1982 ident: 650_CR23 – volume: 320 start-page: 97 year: 1980 ident: 650_CR20 publication-title: J. Reine Angew. Math. – ident: 650_CR10 – volume-title: Topological Vector Spaces. Cambridge Tracts in Mathematics and Mathematical Physics year: 1964 ident: 650_CR13 – ident: 650_CR6 doi: 10.1007/BFb0070913 – ident: 650_CR24 doi: 10.1201/9781003072577-18 – ident: 650_CR7 doi: 10.1007/978-3-642-61715-7 – volume: 287 start-page: 10 issue: 1 year: 2014 ident: 650_CR5 publication-title: Math. Nachr. doi: 10.1002/mana.201200258 – ident: 650_CR9 doi: 10.1090/memo/0016 – ident: 650_CR17 – ident: 650_CR15 doi: 10.1007/BF02787718 – volume: 177 start-page: 463 issue: 4 year: 1981 ident: 650_CR22 publication-title: Math. Z. doi: 10.1007/BF01219081 – ident: 650_CR12 doi: 10.1016/j.jmaa.2013.02.041 – ident: 650_CR14 doi: 10.1007/978-1-4612-1468-7 – volume-title: Explicit Representations of Spaces of Smooth Functions and Distributions year: 2013 ident: 650_CR3 – volume-title: Locally Convex Spaces year: 1981 ident: 650_CR11 doi: 10.1007/978-3-322-90559-8 – ident: 650_CR21 – ident: 650_CR4 doi: 10.4064/dm495-0-1 – ident: 650_CR19 doi: 10.1007/BFb0097765 – ident: 650_CR2 doi: 10.4064/dm495-0-1 – volume: 602 start-page: 123 year: 2007 ident: 650_CR8 publication-title: J. Reine Angew. Math. |
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2013
) there are two gaps. We fill in these gaps by proving... |
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| Title | Completing the Valdivia–Vogt tables of sequence-space representations of spaces of smooth functions and distributions |
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