On compositions of d.c. functions and mappings

Details On compositions of d.c. functions and mappings On compositions of d.c. functions and mappings

2007-06-05

arxiv.org/abs/0706.0624v1

Mathematics

Functional Analysis

19 pages

Scientific paper

A d.c. (delta-convex) function on a normed linear space is a function representable as a difference of two continuous convex functions. We show that an infinite dimensional analogue of Hartman's theorem on stability of d.c. functions under compositions does not hold in general. However, we prove that it holds in some interesting particular cases. Our main results about compositions are proved in the more general context of d.c. mappings between normed linear spaces.

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