Differentiability and best local approximation

Héctor H. Cuenya ^[1] ; Claudia N. Rodriguez ^[1]
1. [1] Universidad Nacional de Río Cuarto
  
  Universidad Nacional de Río Cuarto
  
  Argentina
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 54, Nº. 1, 2013, págs. 15-25
Idioma: inglés
Enlaces
- Texto completo (pdf)
Resumen
- In this paper we give sufficient conditions over the differentiability of a function to assure existence of the best local approximant in Lp-spaces, 0 < p ≤ ∞. These conditions are weaker than those given in previous papers. For p = 2 we show that, in a certain way, they are also necessary. In addition, we characterize the best local approximant.