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

Autores

  • Marcia Sayuri Kashimoto Universidade Federal de Itajubá

DOI:

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

Palavras-chave:

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

Resumo

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.

Biografia do Autor

Marcia Sayuri Kashimoto, Universidade Federal de Itajubá

Referências

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.

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Publicado

2018-12-17

Como Citar

Kashimoto, M. S. (2018). Applications of Nachbin’s Theorem concerning Dense Subalgebras of Differentiable Functions. Trends in Computational and Applied Mathematics, 19(3), 465. https://doi.org/10.5540/tema.2018.019.03.465

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Artigo Original