Applications of Nachbin's Theorem concerning Dense Subalgebras of Differentiable Functions

Marcia Sayuri Kashimoto

Abstract


In this paper, we give some applications of  Nachbin's Theorem  to approximation and interpolation in the the space of all k times continuously differentiable real functions on  any open subset of the  Euclidean space.

Keywords


Nachbin's theorem; approximation of differentiable functions; Stone-Weierstrass theorem

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References


F. Deutsch, Simultaneous interpolation and

approximation in linear topological spaces, SIAM J. Appl. Math.,

(1966), 1180--1190.

M. Moskowitz, F. Paliogiannis, "Functions of Several Real Variables", World Scientific, Singapore, 2011.

J. Mujica, Sub'algebras densas de funciones diferenciables, Cubo Matemática Educacional, 3 (2001), 121--128.

L. Nachbin, Sur les algèbres denses de fonctions différentiables sur une variété, Comptes Rendus de l'Académie des Sciences de Paris, 228 (1949), 1549--1551.

L. Nachbin, " Elements of Approximation Theory", Van Nostrand, Princeton, NJ, 1967, reprinted by Krieger, Huntington, NY, 1976.




DOI: https://doi.org/10.5540/tema.2018.019.03.465

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Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

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