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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Transactions of the American Mathematical Society, vol. 36 (1934), pp. 63–89.
H. Whitney, Derivatives, difference quotients, and Taylor’s formula II, Annals of Mathematics, vol. 35 (1934), pp. 476–485.
H. Whitney, Differentiability of the remainder term in Taylor’s formula, this Journal, vol. 10 (1943), pp. 153–158.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Birkhäuser Boston
About this chapter
Cite this chapter
Whitney, H. (1992). Differentiable Even Functions. In: Eells, J., Toledo, D. (eds) Hassler Whitney Collected Papers. Contemporary Mathematicians. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2972-8_22
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2972-8_22
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7740-8
Online ISBN: 978-1-4612-2972-8
eBook Packages: Springer Book Archive