Global smoothness preservation by singular integrals
DOI:
https://doi.org/10.22199/S07160917.1995.0002.00002Keywords:
Best constant, global smoothness preservation, singular integral, sharp inequality.Abstract
Here is established that the well-known singular integrals of Picard, Poisson-Cauchy and Gauss- Weierstrass fulfill the "global smoothness preservation" property. J. e., they "ripple" less than the function they are applied on, that is producing a nice approximation to the unit. The associated inequalities are sharp.References
[1] S.G. Gal, "Remark on the Degree of Approximation of Continuous Functions by Singular Integrals," Math. Nachr. 164, pp. 197 - 199 (1993).
[2] R.N. Mohapatra and R.S. Rodriguez, "On the Rate of Convergence of Singular Integrals for Holder Continuous Functions," Math. Nachr. 149, pp. 117- 124 (1990).
[2] R.N. Mohapatra and R.S. Rodriguez, "On the Rate of Convergence of Singular Integrals for Holder Continuous Functions," Math. Nachr. 149, pp. 117- 124 (1990).
Published
2018-04-03
How to Cite
[1]
G. A. Anastassiou, “Global smoothness preservation by singular integrals”, Proyecciones (Antofagasta, On line), vol. 14, no. 2, pp. 83-88, Apr. 2018.
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