Equivalence of analytic and rational functions

J. Bochnak; M. Buchner; W. Kucharz

Annales Polonici Mathematici (1997)

  • Volume: 66, Issue: 1, page 37-42
  • ISSN: 0066-2216

Abstract

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We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.

How to cite

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J. Bochnak, M. Buchner, and W. Kucharz. "Equivalence of analytic and rational functions." Annales Polonici Mathematici 66.1 (1997): 37-42. <http://eudml.org/doc/269963>.

@article{J1997,
abstract = {We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.},
author = {J. Bochnak, M. Buchner, W. Kucharz},
journal = {Annales Polonici Mathematici},
keywords = {analytic function; rational function; analytic equivalence},
language = {eng},
number = {1},
pages = {37-42},
title = {Equivalence of analytic and rational functions},
url = {http://eudml.org/doc/269963},
volume = {66},
year = {1997},
}

TY - JOUR
AU - J. Bochnak
AU - M. Buchner
AU - W. Kucharz
TI - Equivalence of analytic and rational functions
JO - Annales Polonici Mathematici
PY - 1997
VL - 66
IS - 1
SP - 37
EP - 42
AB - We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.
LA - eng
KW - analytic function; rational function; analytic equivalence
UR - http://eudml.org/doc/269963
ER -

References

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  1. [1] J. Bochnak, W. Kucharz and M. Shiota, On equivalence of ideals of real global analytic functions and the 17th Hilbert problem, Invent. Math. 63 (1981), 403-421. Zbl0467.32003
  2. [2] J. Bochnak, W. Kucharz and M. Shiota, On algebraicity of global real analytic sets and functions, Invent. Math. 70 (1982), 115-156. Zbl0502.32021
  3. [3] J. Briançon et H. Skoda, Sur la clôture intégrale d’un idéal de germes de fonctions holomorphes en un point de C n , C. R. Acad. Sci. Paris Sér. A 278 (1974), 949-951. Zbl0307.32007
  4. [4] M. Shiota, Equivalence of differentiable mappings and analytic mappings, Inst. Hautes Études Sci. Publ. Math. 54 (1981), 237-322. 
  5. [5] M. Shiota, Equivalence of differentiable functions, rational functions and polynomials, Ann. Inst. Fourier (Grenoble) 32 (1982), 167-204. Zbl0466.58006
  6. [6] R. Thom, L'équivalence d'une fonction différentiable et d'un polynôme, Topology 3 (1965), suppl. 2, 297-307. Zbl0133.30702
  7. [7] J. C. Tougeron, Idéaux de fonctions différentiables, Ergeb. Math. Grenzgeb. 71, Springer, 1972. Zbl0251.58001

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