Spline left fractional monotone approximation involving left fractional differential operators
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 ?<img border=0 width=19 height=19 src="http:/fbpe/img/cubo/v17n1/art05-1.jpg"> of polynomial spli...
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| Autor principal: | |
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| Lenguaje: | English |
| Publicado: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2015
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462015000100005 |
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| Sumario: | 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 ?<img border=0 width=19 height=19 src="http:/fbpe/img/cubo/v17n1/art05-1.jpg"> 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). |
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