| Title:
|
The non-coincidence of ordinary and Peano derivatives (English) |
| Author:
|
Buczolich, Zoltán |
| Author:
|
Weil, Clifford E. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
381-399 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $f H\subset\Bbb R\to\Bbb R$ be $k$ times differentiable in both the usual (iterative) and Peano senses. We investigate when the usual derivatives and the corresponding Peano derivatives are different and the nature of the set where they are different. (English) |
| Keyword:
|
Peano derivatives |
| Keyword:
|
nowhere dense perfect sets |
| Keyword:
|
porosity |
| MSC:
|
26A24 |
| idZBL:
|
Zbl 0936.26002 |
| idMR:
|
MR1722874 |
| DOI:
|
10.21136/MB.1999.125997 |
| . |
| Date available:
|
2009-09-24T21:39:05Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125997 |
| . |
| Reference:
|
[1] H. Fejzić J. Mařík C. E. Weil: Extending Peano derivatives.Math. Bohem. 119 (1994), 387-406. MR 1316592 |
| Reference:
|
[2] V. Jarník: Sur l'extension du domaine de definition des fonctions d'une variable, qui laisse intacte la derivabilité de la fonction.Bull international de l'Acad Sci de Boheme, 1923. |
| Reference:
|
[3] J. Mařík: Derivatives and closed sets.Acta. Math. Acad. Sci. Hungar. 43 (1998), 25-29. MR 0731958 |
| Reference:
|
[4] Clifford E. Weil: The Peano notion of higher order differentiation.Math. Japonica 42 (1995), 587-600. MR 1363850 |
| . |
