Equivalence of analytic and rational functions

• Autorzy: J. Bochnak , M. Buchner , W. Kucharz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

analytic function; rational function; analytic equivalence

Kategorie tematyczne

• 32S20: Global theory of singularities; cohomological properties
• 32B15: Analytic subsets of affine space

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 66
• Numer: 1
• Strony: 37-42

Daty

wydano

1997

otrzymano

1995-06-20

Twórcy

autor

J. Bochnak

• Department of Mathematics, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands

autor

M. Buchner

• Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, U.S.A.

autor

W. Kucharz

• Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, U.S.A.

Bibliografia

• [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.
• [2] J. Bochnak, W. Kucharz and M. Shiota, On algebraicity of global real analytic sets and functions, Invent. Math. 70 (1982), 115-156.
• [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.
• [4] M. Shiota, Equivalence of differentiable mappings and analytic mappings, Inst. Hautes Études Sci. Publ. Math. 54 (1981), 237-322.
• [5] M. Shiota, Equivalence of differentiable functions, rational functions and polynomials, Ann. Inst. Fourier (Grenoble) 32 (1982), 167-204.
• [6] R. Thom, L'équivalence d'une fonction différentiable et d'un polynôme, Topology 3 (1965), suppl. 2, 297-307.
• [7] J. C. Tougeron, Idéaux de fonctions différentiables, Ergeb. Math. Grenzgeb. 71, Springer, 1972.