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

Authors

  • Marcia Sayuri Kashimoto Universidade Federal de Itajubá

DOI:

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

Keywords:

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

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.

Author Biography

Marcia Sayuri Kashimoto, Universidade Federal de Itajubá

Departamento de Matemática e Computação

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.

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Published

2018-12-17

How to Cite

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

Issue

Vol. 19 No. 3 (2018)

Section

Original Article

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