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Search: MSC category 41A05 ( Interpolation [See also 42A15 and 65D05] )

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1. CJM 1998 (vol 50 pp. 1273)

Lubinsky, D. S.
Mean convergence of Lagrange interpolation for exponential weights on $[-1,1]$
We obtain necessary and sufficient conditions for mean convergence of Lagrange interpolation at zeros of orthogonal polynomials for weights on $[-1,1]$, such as \[ w(x)=\exp \bigl(-(1-x^{2})^{-\alpha }\bigr),\quad \alpha >0 \] or \[ w(x)=\exp \bigl(-\exp _{k}(1-x^{2})^{-\alpha }\bigr),\quad k\geq 1, \ \alpha >0, \] where $\exp_{k}=\exp \Bigl(\exp \bigl(\cdots\exp (\ )\cdots\bigr)\Bigr)$ denotes the $k$-th iterated exponential.

Categories:41A05, 42C99

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