Sur le théorème de division de Weierstrass
Chaumat, Jacques ; Chollet, Anne-Marie
Studia Mathematica, Tome 113 (1995), p. 59-84 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We prove a Weierstrass division formula for C∞ Whitney jets ∂̅-flat on arbitrary compact subsets of the complex plane. We also give results for Carleman classes.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:216220 
@article{bwmeta1.element.bwnjournal-article-smv116i1p59bwm,
     author = {Jacques Chaumat and Anne-Marie Chollet},
     title = {Sur le th\'eor\`eme de division de Weierstrass},
     journal = {Studia Mathematica},
     volume = {113},
     year = {1995},
     pages = {59-84},
     zbl = {0839.32002},
     language = {fra},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv116i1p59bwm}
}

Chaumat, Jacques; Chollet, Anne-Marie. Sur le théorème de division de Weierstrass. Studia Mathematica, Tome 113 (1995) pp. 59-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv116i1p59bwm/

[00000] [1] S. Bell and D. Catlin, Proper holomorphic mappings extend smoothly to the boundary, Bull. Amer. Math. Soc. 7 (1982), 269-272. | Zbl 0491.32018

[00001] [2] S. Bell and D. Catlin, Boundary regularity of proper holomorphic mappings, Duke Math. J. 49 (1982), 385-396. | Zbl 0475.32011

[00002] [3] M. D. Bronshteĭn, Division with remainder in spaces of smooth functions, Trans. Moscow Math. Soc. 52 (1990), 109-138.

[00003] [4] J. Bruna, An extension theorem of Whitney type for non-quasianalytic classes of functions, J. London Math. Soc. (2) 22 (1980), 495-505. | Zbl 0419.26010

[00004] [5] J. Chaumat et A. M. Chollet, Noyaux pour résoudre l’équation ∂̅ dans des classes ultradifférentiables sur des compacts irréguliers de ℂm, dans : Several Complex Variables, Proc. Mittag-Leffler Inst. 1987-88, Math. Notes 38, Princeton University Press, 1993, 205-226. | Zbl 0777.32009

[00005] [6] J. Chaumat et A. M. Chollet, Représentations intégrales de jets de Whitney, dans : The Madison Symposium on Complex Analysis, Contemp. Math. 137, Amer. Math. Soc., 1992, 133-153. | Zbl 0768.32001

[00006] [7] J. Chaumat et A. M. Chollet, Théorème de Whitney dans des classes ultradifférentiables, Publ. I.R.M.A. Lille, 1992. | Zbl 0762.26014

[00007] [8] K. Diederich and J. E. Fornæss, Boundary regularity of proper holomorphic mappings, Invent. Math. 67 (1982), 363-384. | Zbl 0501.32010

[00008] [9] E. M. Dynkin, Pseudoanalytic extension of smooth functions. The uniform scale, Amer. Math. Soc. Transl. 115 (1980), 33-58.

[00009] [10] L. Hörmander, The Analysis of Linear Partial Differential Operators I, 2ème éd. Springer, 1989.

[00010] [11] B. Malgrange, Ideals of Differentiable Functions, Oxford University Press, 1966. | Zbl 0177.17902

[00011] [12] W. Pleśniak, Extension and polynomial approximation of ultradifferentiable functions in ℝn, Bull. Soc. Roy. Sci. Liège 63 (1994), 393-402. | Zbl 0816.26009

[00012] [13] V. Thilliez, Prolongement dans des classes ultradifférentiables et propriétés de régularité des compacts de ℝn, Ann. Polon. Math., à paraître.

[00013] [14] J. C. Tougeron, Idéaux de fonctions différentiables, Springer, 1972. | Zbl 0251.58001

[00014] [15] Proceedings of Liverpool Singularities Symposium I, Lecture Notes in Math. 192, Springer, 1971.