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Mean convergence of Lagrange interpolation for exponential weights on $[-1,1]$

  Published:1998-12-01
 Printed: Dec 1998
  • D. S. Lubinsky
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Abstract

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.
MSC Classifications: 41A05, 42C99 show english descriptions Interpolation [See also 42A15 and 65D05]
None of the above, but in this section
41A05 - Interpolation [See also 42A15 and 65D05]
42C99 - None of the above, but in this section
 

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