Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Summary:
It is shown that $n$ times Peano differentiable functions defined on a closed subset of $\mathbb{R}^m$ and satisfying a certain condition on that set can be extended to $n$ times Peano differentiable functions defined on $\mathbb{R}^m$ if and only if the $n$th order Peano derivatives are Baire class one functions.
References:
[ALP1985] V. Aversa, M. Laczkovich, D. Preiss: Extension of differentiable functions. Comment. Math. Univ. Carolin. 26 (1985), 597–609. MR 0817830
[BW1996] Z. Buczolich and C. E. Weil: Extending Peano differentiable functions. Atti Sem. Mat. Fis. Univ. Modena 44 (1996), no. 2, 323–330. MR 1428765
[FMW1994] H. Fejzić, J. Mařík and C. E. Weil: Extending Peano derivatives. Math. Bohemica 119 (1994), 387–406. MR 1316592
[FR1996] H. Fejzić and D. Rinne: Continuity properties of Peano derivatives in several variables. Real Analysis Exch. 21 (1995–96), 292–298. MR 1377538
[H1962] F. Hausdorff: Set Theory. Chelsea, 1962. MR 0141601
[J1923] V. Jarník: Sur l’extension du domaine de definition des fonctions d’une variable, qui laisse intacte la derivabitité de la fonction. Bull international de l’Acad Sci de Boheme (1923).
[M1984] J. Mařík: Derivatives and closed sets. Acta Math. Hungar. 43 (1984), 25–29. DOI 10.1007/BF01951320 | MR 0731958
[PL1974] G. Petruska and M. Lackovich: Baire 1 functions, approximately continuous functions and derivatives. Acta Math. Acad Sci. Hungar. 25 (1974), 189–212. DOI 10.1007/BF01901760 | MR 0379766
[S1970] E. M. Stein: Singular integrals and differentiability properties of functions. Princeton University Press, Princeton, NJ, USA, 1970. MR 0290095 | Zbl 0207.13501
Search
Partner of
