Families of functions dominated by distributions of C -classes of mappings

Goo Ishikawa

Annales de l'institut Fourier (1983)

  • Volume: 33, Issue: 2, page 199-217
  • ISSN: 0373-0956

Abstract

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A subsheaf of the sheaf ℰ Ω of germs C ∞ functions over an open subset Ω of R n is called a sheaf of sub C ∞ function. Comparing with the investigations of sheaves of ideals of ℰ Ω , we study the finite presentability of certain sheaves of sub C ∞ -rings. Especially we treat the sheaf defined by the distribution of Mather’s 𝒞 -classes of a C ∞ mapping.

How to cite

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Ishikawa, Goo. "Families of functions dominated by distributions of $C$-classes of mappings." Annales de l'institut Fourier 33.2 (1983): 199-217. <http://eudml.org/doc/74584>.

@article{Ishikawa1983,
abstract = {A subsheaf of the sheaf $\{\cal E\}_\Omega $ of germs $C^\infty $ functions over an open subset $\Omega $ of $\{\bf R\}^n$ is called a sheaf of sub $C^\infty $ function. Comparing with the investigations of sheaves of ideals of $\{\cal E\}_\Omega $, we study the finite presentability of certain sheaves of sub $C^\infty $-rings. Especially we treat the sheaf defined by the distribution of Mather’s $\{\cal C\}$-classes of a $C^\infty $ mapping.},
author = {Ishikawa, Goo},
journal = {Annales de l'institut Fourier},
keywords = {differential analysis; singularities of differentiable mappings; finite presentability of sheaves},
language = {eng},
number = {2},
pages = {199-217},
publisher = {Association des Annales de l'Institut Fourier},
title = {Families of functions dominated by distributions of $C$-classes of mappings},
url = {http://eudml.org/doc/74584},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Ishikawa, Goo
TI - Families of functions dominated by distributions of $C$-classes of mappings
JO - Annales de l'institut Fourier
PY - 1983
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 2
SP - 199
EP - 217
AB - A subsheaf of the sheaf ${\cal E}_\Omega $ of germs $C^\infty $ functions over an open subset $\Omega $ of ${\bf R}^n$ is called a sheaf of sub $C^\infty $ function. Comparing with the investigations of sheaves of ideals of ${\cal E}_\Omega $, we study the finite presentability of certain sheaves of sub $C^\infty $-rings. Especially we treat the sheaf defined by the distribution of Mather’s ${\cal C}$-classes of a $C^\infty $ mapping.
LA - eng
KW - differential analysis; singularities of differentiable mappings; finite presentability of sheaves
UR - http://eudml.org/doc/74584
ER -

References

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  1. [1] E. J. DUBUC, C∞ schemes, Amer. J. Math., 103 (1981), 683-690. Zbl0483.58003MR83a:58004
  2. [2] A. M. GABRIELOV, Formal relations between analytic functions, Math. USSR. Izv., 7 (1973), 1056-1088. Zbl0297.32007
  3. [3] S. IZUMI, Zeros of ideals of Cr functions, J. Math. Kyoto Univ., 17 (1977), 413-424. Zbl0367.58002MR55 #13470
  4. [4] B. MALGRANGE, Ideals of differentiable functions, Oxford Univ. Press, (1966). 
  5. [5] J. N. MATHER, Stability of C∞ mappings, III : Finitely determined map-germs, Publ. Math. I.H.E.S., 35 (1969), 127-156. Zbl0159.25001
  6. [6] J. MERRIEN, Applications des faiseaux analytiques semi-cohérents aux fonctions différentiables, Ann. Inst. Fourier, 31-1 (1981), 63-82. Zbl0462.58005MR82g:58015
  7. [7] R. MOUSSU and J. Cl. TOUGERON, Fonctions composées analytiques et différentiables, C.R.A.S., Paris, 282 (1976), 1237-1240. Zbl0334.32012MR53 #13628
  8. [8] J. Cl. TOUGERON, An extension of Whitney's spectral theorem, Publ. Math. I.H.E.S., 40 (1971), 139-148. Zbl0239.46023MR51 #6872
  9. [9] J. Cl. TOUGERON, Idéaux de fonctions différentiables, Ergebnisse Der Mathematik, Band 71, Springer (1972). Zbl0251.58001MR55 #13472

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