Hassler Whitney Collected Papers pp 309-310 | Cite as

# Differentiable Even Functions

Chapter

## Abstract

An even function *f* (*x*) = *f* (−*x*) (defined in a neighborhood of the origin) can be expressed as a function *g*(*x* ^{2}); *g*(*u*) is determined for *u* ≥ 0, but not for *u* < 0. We wish to show that *g* may be defined for *u* < 0 also, so that it has roughly half as many derivatives as *f*. A similar result for odd functions is given.

## Bibliography

- 1.H. Whitney,
*Analytic extensions of differentiable functions defined in closed sets*, Transactions of the American Mathematical Society, vol. 36 (1934), pp. 63–89.CrossRefGoogle Scholar - 2.H. Whitney,
*Derivatives, difference quotients, and Taylor’s formula*II, Annals of Mathematics, vol. 35 (1934), pp. 476–485.CrossRefGoogle Scholar - 3.H. Whitney,
*Differentiability of the remainder term in Taylor’s formula*, this Journal, vol. 10 (1943), pp. 153–158.Google Scholar

## Copyright information

© Birkhäuser Boston 1992