Spline left fractional monotone approximation involving left fractional differential operators

• George A Anastassiou ^[1]
  1. [1] University of Memphis

     University of Memphis

     Estados Unidos

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 17, Nº. 1, 2015, págs. 65-73
• Idioma: inglés
• DOI: 10.4067/S0719-06462015000100005
• Enlaces
  • Texto completo
• Resumen
  • español

    Sea f ? Cs ([-1, 1]), s? N y L* un operador diferencial fraccionario lineal izquierdo tal que L* (f) = 0 en [0, 1].. Entonces, existe una sucesión Qn, n ? de splines polinomiales con nodos equiespaciados de un orden fijo dado tal que L* (Qn) = 0 en [0, 1]. Además, f se aproxima con velocidades fraccionales y simult´aneamente por Qn en la norma uniforme. Esta aproximación fraccional restringida a [-1, 1] se encuentra por medio de desigualdades que involucran un módulo alto de suavidad de f(s).

  • English

    Let f ? Cs ([-1, 1]), s? N and L* be a linear left fractional differential operator such that L* (f) = 0 on [0, 1]. Then there exists a sequence Qn, n ? of polynomial splines with equally spaced knots of given fixed order such that L* (Qn) = 0 on [0, 1]. Furthermore f is approximated with rates fractionally and simultaneously by Qn in the uniform norm. This constrained fractional approximation on [-1, 1] is given via inequalities invoving a higher modulus of smoothness of f(s).

• Referencias bibliográficas
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