Mean Convergence of Lagrange Interpolation for Exponential weights on [-1, 1]

Lubinsky, D. S.

Canadian journal of mathematics, Tome 50 (1998) no. 6, pp. 1273-1297

Résumé

We obtain necessary and sufficient conditions for mean convergence of Lagrange interpolation at zeros of orthogonal polynomials for weights on [-1, 1], such as $$w(x)\,=\,\exp \left( -{{\left( 1-{{x}^{2}} \right)}^{-\alpha }} \right),\,\alpha >0$$ or $$w(x)=\exp \left( -{{\exp }_{k}}{{\left( 1-{{x}^{2}} \right)}^{-\alpha }} \right),k\ge 1,\alpha >0,$$ where ${{\exp }_{k}}=\exp \left( \exp \left( \cdot \cdot \cdot \exp (\,)\cdot \cdot \cdot\right) \right)$ denotes the $k$ -th iterated exponential.

Détail

DOI : 10.4153/CJM-1998-062-5

Mots-clés : 41A05, 42C99

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