| Title:
|
Extending Peano derivatives (English) |
| Author:
|
Fejzić, Hajrudin |
| Author:
|
Mařík, Jan |
| Author:
|
Weil, Clifford E. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
119 |
| Issue:
|
4 |
| Year:
|
1994 |
| Pages:
|
387-406 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $H\subset [0,1]$ be a closed set, $k$ a positive integer and $f$ a function defined on $H$ so that the $k$-th Peano derivative relative to $H$ exists. The major result of this paper is that if $H$ has finite Denjoy index, then $f$ has an extension, $F$, to $[0,1]$ which is $k$ times Peano differentiable on $[0,1]$ with $f_i=F_i$ on $H$ for $i=1,2,\ldots,k$. (English) |
| Keyword:
|
Peano derivatives |
| Keyword:
|
Denjoy index |
| MSC:
|
26A24 |
| idZBL:
|
Zbl 0824.26003 |
| idMR:
|
MR1316592 |
| DOI:
|
10.21136/MB.1994.126113 |
| . |
| Date available:
|
2009-09-24T21:07:31Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126113 |
| . |
| Reference:
|
[1] Z. Buczolich: Second Peano derivatives are not extendable.Real Analysis Exch 14 (1988-89), 423-428. MR 0995982, 10.2307/44151957 |
| Reference:
|
[2] P. Bullen: Denjoy's index and porosity.Real Analysis Exch, 10 (1984-84), 85-144. MR 0795610, 10.2307/44151693 |
| Reference:
|
[3] A. Denjoy: Sur l'integration des coefficients differentiels d'order supérieur.Fundamenta Mathematicae 25 (1935), 273-326. 10.4064/fm-25-1-273-326 |
| Reference:
|
[4] M. J. Evans C. E. Weil: Peano derivatives: A survey.Real Analysis Exch, 7(1981-82), 5-24. MR 0646631 |
| Reference:
|
[5] H. Fejzić: Decomposition of Peano derivatives.Proc. Amer. Soc 119 (1993), no. 2, 599-609. MR 1155596, 10.1090/S0002-9939-1993-1155596-8 |
| Reference:
|
[6] H. Fejzić: The Peano derivatives.Doct. Dissertation. Michigan State University, 1992. |
| Reference:
|
[7] H. Fejzić: On generalized Peano and Peano derivatives.Fundamenta Mathematicae 143 (1994), 55-74. MR 1234991, 10.4064/fm-143-1-55-74 |
| Reference:
|
[8] V. Jarník: Sur l'extension du domaine de definition des fonctions d'une variable, qui laisse intacte la derivabilite de la fonction.Bull international de l'Acad Sci de Boheme (1923). |
| Reference:
|
[9] J. Mařík: Derivatives and closed sets.Acta Math. Hung. 43 (1-2) (1984), 25-29. MR 0731958 |
| Reference:
|
[10] G. Petruska, M. Laczkovich: Baire 1 functions, approximately continuous functions and derivatives.Acta Math Acad Sci Hungar, 25 (1974), 189-212. Zbl 0279.26003, MR 0379766, 10.1007/BF01901760 |
| Reference:
|
[11] C. E. Weil: The Peano derivative: What's known and what isn't.Real Analysis Exchange 9 (1983-1984), 354-365. MR 0766061, 10.2307/44153545 |
| . |
