The preparation theorem for composite functions
HTML articles powered by AMS MathViewer
- by Adam Kowalczyk PDF
- Proc. Amer. Math. Soc. 101 (1987), 582-584 Request permission
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
- Th. Bröcker, Differentiable germs and catastrophes, London Mathematical Society Lecture Note Series, No. 17, Cambridge University Press, Cambridge-New York-Melbourne, 1975. Translated from the German, last chapter and bibliography by L. Lander. MR 0494220
- B. Malgrange, Ideals of differentiable functions, Tata Institute of Fundamental Research Studies in Mathematics, vol. 3, Tata Institute of Fundamental Research, Bombay; Oxford University Press, London, 1967. MR 0212575
- John N. Mather, Stability of $C^{\infty }$ mappings. I. The division theorem, Ann. of Math. (2) 87 (1968), 89–104. MR 232401, DOI 10.2307/1970595 V. Poénaru, Singularités ${C^\infty }$ en présence de symétrie, Lecture Notes in Math., vol. 510, Springer-Verlag, Berlin and New York, 1976.
- Gerald W. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975), 63–68. MR 370643, DOI 10.1016/0040-9383(75)90036-1
Additional Information
- © Copyright 1987 American Mathematical Society
- 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