Prolongement dans des classes ultradifférentiables et propriétés de régularité des compacts de ℝn
Vincent Thilliez
Annales Polonici Mathematici, Tome 63 (1996), p. 71-88 / Harvested from The Polish Digital Mathematics Library
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Considering jets, or functions, belonging to some strongly non-quasianalytic Carleman class on compact subsets of ℝn, we extend them to the whole space with a loss of Carleman regularity. This loss is related to geometric conditions refining Łojasiewicz’s “regular separation” or Whitney’s “property (P)”.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:262539 
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     journal = {Annales Polonici Mathematici},
     volume = {63},
     year = {1996},
     pages = {71-88},
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Vincent Thilliez. Prolongement dans des classes ultradifférentiables et propriétés de régularité des compacts de $ℝ^n$
            . Annales Polonici Mathematici, Tome 63 (1996) pp. 71-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv63z1p71bwm/

[000] [Bi] E. Bierstone, Differentiable functions, Bol. Soc. Brasil. Mat. 11 (1980), 139-190. | Zbl 0584.58006

[001] [BBMT] J. Bonet, R. W. Braun, R. Meise and B. A. Taylor, Whitney's extension theorem for nonquasianalytic functions, Studia Math. 99 (1991), 156-184. | Zbl 0738.46009

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

[003] [CC] J. Chaumat et A.-M. Chollet, Théorème de Whitney dans des classes ultra différentiables, Publ. Inst. Rech. Math. Lille 28 (1992), VIII.1-VIII.31 et C. R. Acad. Sci. Paris 315 (1992), 901-906.

[004] [Dr] B. Droste, Holomorphic approximation of ultradifferentiable functions, Math. Ann. 257 (1981), 293-316. | Zbl 0463.32007

[005] [L] A. Lambert, Quelques théorèmes de décomposition des ultradistributions, Ann. Inst. Fourier (Grenoble) 29 (3) (1979), 57-100. | Zbl 0396.46038

[006] [M] B. Malgrange, Ideals of Differentiable Functions, Tata Institute for Fundamental Research, Bombay and Oxford Univ. Press, 1966. | Zbl 0177.17902

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

[008] [T] J.-C. Tougeron, Idéaux de fonctions différentiables, Ergeb. Math. Grenzgeb. 71, Springer, 1972. | Zbl 0251.58001

[009] [Wa] K. Wachta, Prolongation des fonctions C∞, Bull. Polish Acad. Sci. Math. 31 (1983), 245-248. | Zbl 0595.58004

[010] [W] H. Whitney, Functions differentiable on the boundaries of regions, Ann. of Math. 35 (1934), 482-485. | Zbl 60.0217.03