Abstract
In order to approximate functions defined on the real semiaxis, which can grow exponentially both at 0 and at +∞, we introduce a suitable Lagrange operator based on the zeros of orthogonal polynomials with respect to the weight w(x)=xγe−x−α−xβ. We prove that this interpolation process has Lebesgue constant with order logm in weighted uniform metric and converges with the order of the best approximation in a large subset of weighted Lp-spaces, 1<p<∞, with proper assumptions.
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