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On the Extension of Differentiable Functions

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

Abstract

The author has shown previously how to extend the definition of a function of class C m defined in a closed set A so it will be of class C m throughout space (see [l]).1 Here we shall prove a uniformity property: If the function and its derivatives are sufficiently small in A, then they may be made small throughout space.

Keywords

Finite Number Differentiable Function Preceding Theorem Concentric Region Boundedness Condition 
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References

  1. 1.
    H. Whitney,Analytic extensions of differentiable functions defined in closed set,Trans. Amer. Math. Soc. vol. 36 (1934) pp. 63–89.CrossRefGoogle Scholar
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    H. Whitney,Differentiable functions defined in arbitrary subsets of Euclidean space,Trans. Amer. Math. Soc. vol. 40 (1936) pp. 309–317. Further references are given here.CrossRefGoogle Scholar
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    H. O. Hirschfeld,Continuation of differentiable functions through the plane,Quart. J. Math. Oxford Ser. vol. 7 (1936) pp. 1–15.CrossRefGoogle Scholar
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    M. R. Hestenes,Extension of the range of a differentiable function,Duke Math. J. vol. 8 (1941) pp. 183–192.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 1992

Authors and Affiliations

  • Hassler Whitney

There are no affiliations available

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