Extending Peano derivatives: necessary and sufficient conditions
Volume 159 / 1999
Fundamenta Mathematicae 159 (1999), 219-229
DOI: 10.4064/fm-159-3-219-229
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.
