This paper summarizes recent results on weighted polynomial approximations for functions defined on the real semiaxis. The function may grow exponentially both at 0 and at +∞. We discuss orthogonal polynomials, polynomial inequalities, function spaces with new moduli of smoothness, estimates for the best approximation, Gaussian rules, and Lagrange interpolation with respect to the weight w(x)=x^γ e^(−x^(−α)−x^β) (α>0, β>1, γ≥0).
Polynomial approximation with Pollaczeck--Laguerre weights on the real semiaxis. A survey
Notarangelo, Incoronata
2018-01-01
Abstract
This paper summarizes recent results on weighted polynomial approximations for functions defined on the real semiaxis. The function may grow exponentially both at 0 and at +∞. We discuss orthogonal polynomials, polynomial inequalities, function spaces with new moduli of smoothness, estimates for the best approximation, Gaussian rules, and Lagrange interpolation with respect to the weight w(x)=x^γ e^(−x^(−α)−x^β) (α>0, β>1, γ≥0).
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