Hassler Whitney Collected Papers pp 323-328 | Cite as

# On the Extension of Differentiable Functions

Chapter

## 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.H. Whitney,
*Analytic extensions of differentiable functions defined in closed set*,Trans. Amer. Math. Soc. vol. 36 (1934) pp. 63–89.CrossRefGoogle Scholar - 2.H. Whitney,
*Functions differentiable on the boundaries of regions*,Ann. of Math.vol. 35 (1934) pp. 482–485.CrossRefGoogle Scholar - 3.H. Whitney,
*Differentiable manifolds*,Ann. of Math. vol. 37 (1936) pp. 645–680.CrossRefGoogle Scholar - 4.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 - 5.H. O. Hirschfeld,
*Continuation of differentiable functions through the plane*,Quart. J. Math. Oxford Ser. vol. 7 (1936) pp. 1–15.CrossRefGoogle Scholar - 6.M. R. Hestenes,
*Extension of the range of a differentiable function*,Duke Math. J. vol. 8 (1941) pp. 183–192.CrossRefGoogle Scholar

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© Birkhäuser Boston 1992