The paper deals with weighted polynomial approximation for functions defined on $(-1,1)$, which can grow exponentially both at $-1$ and at $1$. We summarize recent results on function spaces with new moduli of smoothness, estimates for the best approximation, Lagrange interpolation, Fourier sums and Gaussian rules with respect to weights of the form $w(x)=(1-x^2)^eta exp{-(1-x^2)^{-alpha}}$.
Polynomial approximation with Pollaczek-type weights. A survey
NOTARANGELO, Incoronata
2020-01-01
Abstract
The paper deals with weighted polynomial approximation for functions defined on $(-1,1)$, which can grow exponentially both at $-1$ and at $1$. We summarize recent results on function spaces with new moduli of smoothness, estimates for the best approximation, Lagrange interpolation, Fourier sums and Gaussian rules with respect to weights of the form $w(x)=(1-x^2)^eta exp{-(1-x^2)^{-alpha}}$.
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