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ArticleOriginal scientific text

Title

Extending Peano derivatives: necessary and sufficient conditions

Authors 1

Affiliations

  1. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201 U.S.A.

Abstract

The paper treats functions which are defined on closed subsets of [0,1] and which are k times Peano differentiable. A necessary and sufficient condition is given for the existence of a k times Peano differentiable extension of such a function to [0,1]. Several applications of the result are presented. In particular, functions defined on symmetric perfect sets are studied.

Bibliography

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Fundamenta Mathematicae
1999/159/3
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Pages:
219-229
Main language of publication
English
Received
1997-06-18
Accepted
1998-02-02
Published
1999
Exact and natural sciences