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The preparation theorem for composite functions


Author: Adam Kowalczyk
Journal: Proc. Amer. Math. Soc. 101 (1987), 582-584
MSC: Primary 58C27; Secondary 57R45, 57S15
DOI: https://doi.org/10.1090/S0002-9939-1987-0908673-5
MathSciNet review: 908673
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Abstract: We present a simple extension of the preparation theorem of B. Malgrange and J. Mather to the case of composite functions. As a corollary we obtain a short proof of the equivariant preparation theorem of V. Poénaru.


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

  • [1] Th. Bröcker, Differentiable germs and catastrophes, Cambridge University Press, Cambridge-New York-Melbourne, 1975. Translated from the German, last chapter and bibliography by L. Lander; London Mathematical Society Lecture Note Series, No. 17. MR 0494220
  • [2] B. Malgrange, Ideals of differentiable functions, Tata Institute of Fundamental Research Studies in Mathematics, No. 3, Tata Institute of Fundamental Research, Bombay; Oxford University Press, London, 1967. MR 0212575
  • [3] John N. Mather, Stability of 𝐶^{∞} mappings. I. The division theorem, Ann. of Math. (2) 87 (1968), 89–104. MR 0232401, https://doi.org/10.2307/1970595
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  • [5] Gerald W. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975), 63–68. MR 0370643, https://doi.org/10.1016/0040-9383(75)90036-1

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0908673-5
Keywords: Preparation theorem, Malgrange division theorem, equivariant division theorem, composite functions
Article copyright: © Copyright 1987 American Mathematical Society