Approximation in different smoothness spaces with the RAFU method
Keywords:RAFU method, RAFU approximation, Approximation Theory
The RAFU method is an original and unknown approximation procedure we can use in Approximation Theory. We know that the RAFU method provides a linear space uniformly dense in C[a,b] by using some separation conditions. In this work, we will show we can employ the RAFU method to approximate functions of C0(R) and C00(R), Riemann integrable functions, Lebesgue integrable functions, functions of Lp[a,b] and Lp(R), 1≤p<¥ and measurable functions. Moreover, Riemann integrals can be approximated by the integrals of the functions that the RAFU method provides.
D. L. Cohn, Measure Theory, Birkhäuser, 1980. https://doi.org/10.1007/978-1-4899-0399-0
E. Corbacho, A RAFU linear space uniformly dense in C[a,b], Appl. Gen. Topology 14, no. 1 (2013), 53-60. https://doi.org/10.4995/agt.2013.1617
E. Corbacho, Uniform approximation with radical functions, SeMA Journal 58, (2012), 97-122. https://doi.org/10.1007/BF03322606
E. Corbacho, Uniform reconstruction of continuous functions with the RAFU method. Error bounds. Algorithms., submitted
J. L. Blasco and A. Moltó, On the uniform closure of a linear space of bounded real-valued functions, Annali di Matematica Pura ed Applicata IV, vol. CXXXIV (1983), 233-239. https://doi.org/10.1007/BF01773506
M. I. Garrido and F. Montalvo, Uniform approximation theorems for real-valued continuous functions, Topology Appl. 45 (1992), 145-155. https://doi.org/10.1016/0166-8641(92)90054-4
T. Gassó, S. Hernández and E. Rojas, Representation and approximation by series of continuous functions, Acta Math. Hungar. 123, no. 1-2 (2009), 91-102. https://doi.org/10.1007/s10474-008-8064-z
How to Cite
This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.