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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
DOI: https://doi.org/10.1090/S0002-9939-1979-0532164-2
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.


References [Enhancements On Off] (What's this?)

  • [1] R. Abraham and J. Robbin, Transversal mappings and flows, Benjamin, New York, 1967. MR 0240836 (39:2181)
  • [2] Dang Dình Áng and Vũ Trong Tuan, An elementary proof of the Morse-Palais lemma for Banach spaces, Proc. Amer. Math. Soc. 39 (1973), 642-644. MR 0319225 (47:7770)
  • [3] N. Kuiper, $ {C^2}$-functions near nondegenerate critical points unpublished manuscript.
  • [4] R. S. Palais, Morse theory on Hilbert manifolds, Topology 2 (1963), 240-299. MR 0158410 (28:1633)
  • [5] -, The Morse lemma on Banach spaces, Bull. Amer. Math. Soc. 75 (1969), 968-971. MR 0253378 (40:6593)
  • [6] A. J. Tromba, The Morse lemma on Banach spaces, Proc. Amer. Math. Soc. 34 (1972), 396-402. MR 0295395 (45:4461)
  • [7] -, The Morse lemma on arbitrary Banach spaces, Bull. Amer. Math. Soc. 79 (1973), 85-36. MR 0305437 (46:4567)
  • [8] -, Almost Riemannian structures on Banach manifolds: The Morse lemma and the Darboux theorem, Canad. J. Math. 38 (1976), 640-652. MR 0402799 (53:6613)
  • [9] H. Whitney, Differentiability of the remainder term in Taylor's formula, Duke Math. J. 10 (1943), 153-158. MR 0007782 (4:192e)

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Additional Information

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

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