On functions representable as a difference of convex functions

When x is a real variable, so that D is a (bounded or unbounded) interval, then f(x) is a d.c. function if and only if / has left and right derivatives (where these are meaningful) and these derivatives are of bounded variation on every closed bounded interval interior to D. Straus remarked that this fact implies that if flx)9flx) are d.c. functions of a real variable, then so are the product fix) fix), the quotient flx)lflx) when fix) Φ 0, and the composite flflx)) under suitable conditions on /2. He raised the question whether or not this remark can be extended to cases where x is a variable on a more general space. The object of this note is to give an affirmative answer to this question if x is a point in a finite dimensional (Euclidean) space.