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

Marcia Sayuri Kashimoto


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.


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

Full Text:



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.

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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.


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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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