Global smoothness preservation by singular integrals

• Anastassiou, George A. ^[1]
  1. [1] Memphis State University.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 14, Nº. 2, 1995, págs. 83-88
• Idioma: inglés
• DOI: 10.22199/S07160917.1995.0002.00002
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• Resumen

  • 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.

• Referencias bibliográficas
  • Citas [1] S.G. Gal, "Remark on the Degree of Approximation of Continuous Functions by Singular Integrals," Math. Nachr. 164, pp....
  • [2] R.N. Mohapatra and R.S. Rodriguez, "On the Rate of Convergence of Singular Integrals for Holder Continuous Functions," Math. Nachr....