Sur la division et la composition dans des classes ultradifférentiables

Jacques Chaumat; Anne-Marie Chollet

Studia Mathematica (1999)

  • Volume: 136, Issue: 1, page 49-70
  • ISSN: 0039-3223

Abstract

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We generalize to some classes of ultradifferentiable jets or functions the classical Łojasiewicz Division Theorem and Glaeser Composition Theorem. The proof uses the desingularization results by Hironaka, Bierstone and Milman.

How to cite

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Chaumat, Jacques, and Chollet, Anne-Marie. "Sur la division et la composition dans des classes ultradifférentiables." Studia Mathematica 136.1 (1999): 49-70. <http://eudml.org/doc/216660>.

@article{Chaumat1999,
author = {Chaumat, Jacques, Chollet, Anne-Marie},
journal = {Studia Mathematica},
keywords = {division and composition theorems; ultradifferentiable functions; Whitney jets; Gevrey classes},
language = {fre},
number = {1},
pages = {49-70},
title = {Sur la division et la composition dans des classes ultradifférentiables},
url = {http://eudml.org/doc/216660},
volume = {136},
year = {1999},
}

TY - JOUR
AU - Chaumat, Jacques
AU - Chollet, Anne-Marie
TI - Sur la division et la composition dans des classes ultradifférentiables
JO - Studia Mathematica
PY - 1999
VL - 136
IS - 1
SP - 49
EP - 70
LA - fre
KW - division and composition theorems; ultradifferentiable functions; Whitney jets; Gevrey classes
UR - http://eudml.org/doc/216660
ER -

References

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  1. [1] M. F. Atiyah, Resolution of singularities and division of distributions, Comm. Pure Appl. Math. 23 (1970), 145-150. Zbl0188.19405
  2. [2] I. N. Bernstein and S. I. Gel’fand, Meromorphic property of the function P λ , Funct. Anal. Appl. 3 (1969), 68-69. 
  3. [3] E. Bierstone and P. D. Milman, Semianalytic and subanalytic sets, Publ. I.H.E.S. 67 (1988), 5-42. Zbl0674.32002
  4. [4] E. Bierstone and P. D. Milman, A simple constructive proof of canonical resolution of singularities, in: Effective Methods in Algebraic Geometry, Progr. Math. 94, Birkhäuser, 1991, 11-30. Zbl0743.14012
  5. [5] L. P. Bos and P. D. Milman, Sobolev-Gagliardo-Nirenberg and Markov type inequalities on subanalytic domains, Geom. Funct. Anal. 5 (1995), 853-923. Zbl0848.46022
  6. [6] J. Chaumat et A.-M. Chollet, Propriétés de l'intersection des classes de Gevrey et de certaines autres classes, Bull. Sci. Math. (1998), à paraître. 
  7. [7] G. Glaeser, Fonctions composées différentiables, Ann. of Math. 77 (1963), 193-209. Zbl0106.31302
  8. [8] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, ibid. 79 (1964), 109-326. 
  9. [9] S. Łojasiewicz, Sur le problème de la division, Studia Math. 8 (1959), 87-136. Zbl0115.10203
  10. [10] B. Malgrange, Ideals of Differentiable Functions, Oxford Univ. Press, 1966. 
  11. [11] V. Thilliez, Sur les fonctions composées différentiables, J. Math. Pures Appl. 76 (1997), 499-524. 
  12. [12] J. C. Tougeron, Idéaux de fonctions différentiables, Springer, 1972. Zbl0251.58001

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