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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A representation theorem for differentiable functions


Authors: Vũ Trọng Tuấn and Ðǎng Ðình Áng
Journal: Proc. Amer. Math. Soc. 75 (1979), 343-350
MSC: Primary 58C25; Secondary 58E05
MathSciNet review: 532164
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Abstract: The authors give a representation formula for differentiable functions analogous to Taylor's formula, but in which the differentiability of the remainder term is recovered. The result is used to prove a generalization of the Morse lemma.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0532164-2
Keywords: Whitney's theorem on differentiability of the remainder term in Taylor's formula, Morse lemma
Article copyright: © Copyright 1979 American Mathematical Society