Global Cm - approximations in Rk

• Autorzy: Jurzak J. -P.
• Języki publikacji: EN

Abstrakty

EN

The convolution of a function f ∈ Cm(Rk ;R) with a Dirac-sequence gives an approximation of f ∈ C°(Rk ;R) by a sequence of functions fn ∈ C∞(Rk ;R) n ≥ 1 converging uniformly on compact subsets of Rk as well as its derivatives. The paper studies global estimations on Rk , i.e. there exists functions hα ∈ C∞(Rk ; R) and a sequence εα(n) → 0 such that [wzór] for all x ∈ Rk, all | α |≤ m and all n ≥ 1. Special subalgebras of C∞(Rk ;R) are introduced for the study of the dominated behavior of the convolution process. Some extensions for Cm(Ω ;R) are obtained with Ω open subset of Rk.

Słowa kluczowe

EN

convolution; approximations; dominated convergence

PL

splot; przybliżenie(aproksymacja); zbieżność majoryzowana

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2004
• Tom: Vol. 10, nr 2
• Strony: 291--302
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Jurzak J. -P.

• Laboratoire Gevrey De Mathematique Physique Universite De Bourgogne Faculte Des Sciences Et Techniques BP 47870, 21078 Dijon Cedex France,

Bibliografia

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• [2] Grothendieck, A., Topological Vector Spaces, Gordon and Breach Science Publisher, New York-London-Paris, 1973.
• [3] Grothendieck, A., Sur les espaces (Ƒ) et (ƊƑ), Summa Brasil. Math. 3(6) (1954), 57-123.
• [4] Jurzak, J.-P., Un aspect fonctionnel de l’intégration, C. R. Acad. Sci. Paris Ser. I Math. 296 (1983), 589-591.
• [5] Jurzak, J.-P., Unbounded Non-Commutative Integration, Math. Phys. Stud. 7, Kluwer Acad. Publ., Dordrecht, 1985.
• [6] Jurzak, J.-P., Uniform dominated convergence and Stone-Weierstrass theorem, preprint, 2003, 1-14.
• [7] Treves, F., Topological Vector Spaces, Distributions and Kernels, Academic Press, New-York, 1967.