A RAFU linear space uniformly dense in C [a, b]

Eduardo Corbacho Cortés

Spain

University of Extremadura

Department of Mathematics

Submitted: 2013-07-26

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Accepted: 2013-07-26

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DOI: https://doi.org/10.4995/agt.2013.1617
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Keywords:

RAFU, Uniform density, Uniform approximation, Radical functions, Approximation algorithm

Supporting agencies:

This research was not funded

Abstract:

In this paper we prove that a RAFU (radical functions) linear space, âˆ, is uniformly dense in C [a, b] by means of a S-separation condition of certain subsets of [a, b] due to Blasco-Moltó. This linear space is not a lattice or an algebra. Given an arbitrary function f 2 C [a, b] we will obtain easily the sequence (Cn)n of ∠that converges uniformly to f and we will show the degree of uniform approximation to f with (Cn)n.
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References:

E. Corbacho, Teoría general de la aproximación mediante funciones radicales, ISBN 84-690-1149-9, (Mérida, 2006).

E. Corbacho, The degree of uniform approximation by radical funtions, XXII CEDYA- XII CMA, September 5th-9th, (Palma de Mallorca, 2011).

E. Corbacho, Uniform approximation by means of radical functions, I Jaen Conference on Approximation Theory, July 4th-9th, (Jaen, 2010).

G. J. O. Jameson, Topology and normed spaces, Chapman and Hall, (London, 1974).

H. Tietze, Uber functionen die anf einer abgeschlossenen menge stetig sind, Journ. Math. 145 (1915), 9-14. https://doi.org/10.1515/crll.1915.145.9

J. L. Blasco and A. Moltó, On the uniform closure of a linear space of bounded realvalued functions, Annali di Matematica Pura ed Applicata IV vol. CXXXIV (1983), 233-239. https://doi.org/10.1007/BF01773506

M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375-481.

https://doi.org/10.1090/S0002-9947-1937-1501905-7

M. I. Garrido, Aproximación uniforme en espacios de funciones continuas, Publicaciones del Departamento de Matemáticas Universidad de Extremadura 24, ( Univ. Extremadura, Badajoz 1990).

M. T. Gassó, S. Hernández and S. Rojas, Aproximación por series en espacios de funciones continuas, (Univesitat Jaume I, Departament de Matemátiques, 2010).

S. Kakutani, Concrete representation of abstract (M)-spaces, Ann. Math. 42 (1941), 994-1024. https://doi.org/10.2307/1968778

S. Mrowka, On some approximation theorems, Nieuw Archief voor Wiskunde (3) XVI (1968), 94-111.

S. Stone, A generalized Weierstrass approximation theorem, Math. Magazine 21 (1948) 167-184, 237-254. https://doi.org/10.2307/3029750

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