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Differentiable Even Functions

  • Hassler Whitney
Part of the Contemporary Mathematicians book series (CM)

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. 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. 2.
    H. Whitney, Derivatives, difference quotients, and Taylor’s formula II, Annals of Mathematics, vol. 35 (1934), pp. 476–485.CrossRefGoogle Scholar
  3. 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

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  • Hassler Whitney

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