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Differentiability of Peano derivatives


Author: Andreas Fischer
Journal: Proc. Amer. Math. Soc. 136 (2008), 1779-1785
MSC (2000): Primary 26B05
DOI: https://doi.org/10.1090/S0002-9939-07-09320-3
Published electronically: December 18, 2007
MathSciNet review: 2373608
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Abstract | References | Similar Articles | Additional Information

Abstract: Peano differentiability is a notion of higher-order Fréchet differentiability. H. W. Oliver gave sufficient conditions for the $ m^{{th}}$ Peano derivative to be a Fréchet derivative in the case of functions of a real variable. Here we generalize this theorem to functions of several variables.


References [Enhancements On Off] (What's this?)

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  • 2. Kurdyka, Krzysztof; Pawłucki, Wiesław, Subanalytic version of Whitney's extension theorem. Studia Math. 124 (1997), no. 3, 269-280. MR 1456425 (98i:32008)
  • 3. Oliver, H. William, The exact Peano derivative. Trans. Amer. Math. Soc. 76 (1954), 444-456. MR 0062207 (15:944d)
  • 4. Peano, G., Sulla formula di Taylor. (Italian) Torino Atti XXVII. 40-46. (1891).

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Additional Information

Andreas Fischer
Affiliation: Department of Mathematics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan S7N 5E6, Canada
Email: el.fischerandreas@web.de

DOI: https://doi.org/10.1090/S0002-9939-07-09320-3
Received by editor(s): October 28, 2005
Received by editor(s) in revised form: April 17, 2006
Published electronically: December 18, 2007
Additional Notes: The author’s research was supported by EC-IHP-Network RAAG (Contract-No: HPRN-CT-2001-00271)
Communicated by: David Preiss
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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