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  • 1 Loránd Eötvös University Department Of Numerical Analysis H-1117 Budapest Pázmány P. Sétány I/C H-1117 Budapest Pázmány P. Sétány I/C
  • | 2 Hungarian Academy of Sciences Alfréd Rényi Institute of Mathematics Alfréd Rényi Institute of Mathematics H-1053 Budapest Reáltanoda U. 13--15 H-1053 Budapest Reáltanoda U. 13--15
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Abstract  

The aim of this paper is to continue our investigations started in [15], where we studied the summability of weighted Lagrange interpolation on the roots of orthogonal polynomials with respect to a weight function w. Starting from the Lagrange interpolation polynomials we constructed a wide class of discrete processes which are uniformly convergent in a suitable Banach space (Cρ, ‖‖ρ) of continuous functions (ρ denotes (another) weight). In [15] we formulated several conditions with respect to w, ρ, (Cρ, ‖‖ρ) and to summation methods for which the uniform convergence holds. The goal of this part is to study the special case when w and ρ are Freud-type weights. We shall show that the conditions of results of [15] hold in this case. The order of convergence will also be considered.

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