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.
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References
H. Whitney,Analytic extensions of differentiable functions defined in closed set,Trans. Amer. Math. Soc. vol. 36 (1934) pp. 63–89.
H. Whitney,Functions differentiable on the boundaries of regions,Ann. of Math.vol. 35 (1934) pp. 482–485.
H. Whitney,Differentiable manifolds,Ann. of Math. vol. 37 (1936) pp. 645–680.
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.
H. O. Hirschfeld,Continuation of differentiable functions through the plane,Quart. J. Math. Oxford Ser. vol. 7 (1936) pp. 1–15.
M. R. Hestenes,Extension of the range of a differentiable function,Duke Math. J. vol. 8 (1941) pp. 183–192.
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© 1992 Birkhäuser Boston
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Whitney, H. (1992). On the Extension of Differentiable 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_24
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DOI: https://doi.org/10.1007/978-1-4612-2972-8_24
Publisher Name: Birkhäuser Boston
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