Characterizations of derivations on spaces of smooth functions
We provide a list of equivalent conditions under which an additive operator acting on a space of smooth functions on a compact real interval is a multiple of the derivation.
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| Veröffentlicht in: | Aequationes mathematicae Jg. 97; H. 4; S. 777 - 786 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Cham
Springer International Publishing
01.08.2023
Springer Nature B.V |
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| ISSN: | 0001-9054, 1420-8903 |
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| Abstract | We provide a list of equivalent conditions under which an additive operator acting on a space of smooth functions on a compact real interval is a multiple of the derivation. |
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| AbstractList | We provide a list of equivalent conditions under which an additive operator acting on a space of smooth functions on a compact real interval is a multiple of the derivation. |
| Author | Fechner, Włodzimierz Świątczak, Aleksandra |
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| References | Kurepa (CR13) 1964; 19 Kannappan, Kurepa (CR9) 1970; 4 Ebanks (CR4) 2019; 74 Gselmann (CR6) 2019; 539 CR12 Nishiyama, Horinouchi (CR14) 1968; 1 Jurkat (CR8) 1965; 16 Ebanks (CR2) 2019; 93 König, Milman (CR11) 2018 Gselmann (CR5) 2012; 78 Amou (CR1) 2019; 93 Gselmann, Kiss, Vincze (CR7) 2018; 73 Kannappan, Kurepa (CR10) 1971; 6 Ebanks (CR3) 2019; 93 A Nishiyama (934_CR14) 1968; 1 M Amou (934_CR1) 2019; 93 934_CR12 B Ebanks (934_CR4) 2019; 74 P Kannappan (934_CR9) 1970; 4 E Gselmann (934_CR6) 2019; 539 P Kannappan (934_CR10) 1971; 6 E Gselmann (934_CR7) 2018; 73 E Gselmann (934_CR5) 2012; 78 WB Jurkat (934_CR8) 1965; 16 H König (934_CR11) 2018 S Kurepa (934_CR13) 1964; 19 B Ebanks (934_CR2) 2019; 93 B Ebanks (934_CR3) 2019; 93 |
| References_xml | – volume: 16 start-page: 683 year: 1965 end-page: 686 ident: CR8 article-title: On Cauchy’s functional equation publication-title: Proc. Am. Math. Soc. – volume: 93 start-page: 1127 issue: 6 year: 2019 end-page: 1138 ident: CR3 article-title: Derivations and Leibniz differences on rings: II publication-title: Aequ. Math. doi: 10.1007/s00010-018-0630-z – volume: 78 start-page: 137 issue: 1–2 year: 2012 end-page: 145 ident: CR5 article-title: Notes on the characterization of derivations publication-title: Acta Sci. Math. (Szeged) doi: 10.1007/BF03651308 – volume: 539 start-page: 65 year: 2019 ident: CR6 article-title: Characterizations of derivations publication-title: Diss. Math. – volume: 73 start-page: 1 issue: 2 year: 2018 end-page: 27 ident: CR7 article-title: On functional equations characterizing derivations: methods and examples publication-title: Results Math. doi: 10.1007/s00025-018-0833-6 – volume: 19 start-page: 23 year: 1964 end-page: 36 ident: CR13 article-title: The Cauchy functional equation and scalar product in vector spaces publication-title: Glasnik Mat.-Fiz. Astronom. Društvo Mat. Fiz. Hrvatske Ser. II – ident: CR12 – volume: 6 start-page: 46 year: 1971 end-page: 58 ident: CR10 article-title: Some relations between additive functions. II publication-title: Aequ. Math. doi: 10.1007/BF01833237 – volume: 1 start-page: 1 year: 1968 end-page: 5 ident: CR14 article-title: On a system of functional equations publication-title: Aequ. Math. doi: 10.1007/BF01817553 – year: 2018 ident: CR11 publication-title: Operator Relations Characterizing Derivatives doi: 10.1007/978-3-030-00241-1 – volume: 74 start-page: 1 issue: 4 year: 2019 end-page: 12 ident: CR4 article-title: Functional equations characterizing derivations and homomorphisms on fields publication-title: Results Math. doi: 10.1007/s00025-019-1063-2 – volume: 4 start-page: 163 year: 1970 end-page: 175 ident: CR9 article-title: Some relations between additive functions. I publication-title: Aequ. Math. doi: 10.1007/BF01817757 – volume: 93 start-page: 345 issue: 2 year: 2019 end-page: 350 ident: CR1 article-title: Multiadditive functions satisfying certain functional equations publication-title: Aequ. Math. doi: 10.1007/s00010-018-0627-7 – volume: 93 start-page: 629 issue: 3 year: 2019 end-page: 640 ident: CR2 article-title: Derivations and Leibniz differences on rings publication-title: Aequ. Math. doi: 10.1007/s00010-018-0601-4 – volume: 93 start-page: 1127 issue: 6 year: 2019 ident: 934_CR3 publication-title: Aequ. Math. doi: 10.1007/s00010-018-0630-z – volume: 1 start-page: 1 year: 1968 ident: 934_CR14 publication-title: Aequ. Math. doi: 10.1007/BF01817553 – ident: 934_CR12 doi: 10.1007/978-3-7643-8749-5 – volume: 78 start-page: 137 issue: 1–2 year: 2012 ident: 934_CR5 publication-title: Acta Sci. Math. (Szeged) doi: 10.1007/BF03651308 – volume: 4 start-page: 163 year: 1970 ident: 934_CR9 publication-title: Aequ. Math. doi: 10.1007/BF01817757 – volume: 93 start-page: 345 issue: 2 year: 2019 ident: 934_CR1 publication-title: Aequ. Math. doi: 10.1007/s00010-018-0627-7 – volume: 16 start-page: 683 year: 1965 ident: 934_CR8 publication-title: Proc. Am. Math. Soc. – volume: 73 start-page: 1 issue: 2 year: 2018 ident: 934_CR7 publication-title: Results Math. doi: 10.1007/s00025-018-0833-6 – volume: 74 start-page: 1 issue: 4 year: 2019 ident: 934_CR4 publication-title: Results Math. doi: 10.1007/s00025-019-1063-2 – volume: 539 start-page: 65 year: 2019 ident: 934_CR6 publication-title: Diss. Math. – volume: 93 start-page: 629 issue: 3 year: 2019 ident: 934_CR2 publication-title: Aequ. Math. doi: 10.1007/s00010-018-0601-4 – volume: 6 start-page: 46 year: 1971 ident: 934_CR10 publication-title: Aequ. Math. doi: 10.1007/BF01833237 – volume-title: Operator Relations Characterizing Derivatives year: 2018 ident: 934_CR11 doi: 10.1007/978-3-030-00241-1 – volume: 19 start-page: 23 year: 1964 ident: 934_CR13 publication-title: Glasnik Mat.-Fiz. Astronom. Društvo Mat. Fiz. Hrvatske Ser. II |
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| Title | Characterizations of derivations on spaces of smooth functions |
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