Linfin convergence of interpolation and associated product integration for exponential weights

investigate convergence in a weighted L∞ norm of Hermite, Hermite, and Grunwald interpolations at zeros of orthogonal polynomials with respect to exponential weights such as Freud, Erdos, and exponential weight on (-1, 1). Convergence of product integration rules induced by the various approximation processes is deduced. We also give more precise weight conditions for convergence of interpolations with respect to above three types of weights, respectively.

[1]  V. Totik,et al.  Moduli of smoothness , 1987 .

[2]  D. Lubinsky,et al.  Hermite and Hermite-Feje´r interpolation and associated product integration rules on the real line: the L ∞ theory , 1992 .

[3]  J. Szabados.  Fej r Interpolation on the Real Line , 1997 .

[4]  On mean convergence of Hermite–Fejér and Hermite interpolation for Erdős weights , 1998 .

[5]  The Weighted Lp-Norms of Orthonormal Polynomials for Freud Weights , 1994 .

[6]  Necessary and sufficient conditions for mean convergence of Lagrange interpolation for Freud weights , 1995 .

[7]  Doron S. Lubinsky,et al.  Erratum: Christoffel functions, orthogonal polynomials, and Nevai's conjecture for Freud weights , 1992 .

[8]  A. Levin,et al.  Christoffel functions and orthogonal polynomials for exponential weights on [-1,1] , 1994 .

[9]  J. Szabados,et al.  Weighted Lagrange and Hermite–Fejér interpolation on the real line , 1997 .

[10]  Steven B. Damelin.  The Weighted Lebesgue Constant of Lagrange Interpolation for Exponential Weights on [-1, 1] , 1998 .

[11]  Mean convergence of Hermite-Feje´r and Hermite interpolation for Freud weights , 1998 .

[12]  S. Damelin,et al.  Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Erdős Weights , 1993, Canadian Journal of Mathematics.

[13]  Rene F. Swarttouw,et al.  Orthogonal polynomials , 2020, NIST Handbook of Mathematical Functions.

[14]  The weighted Lp-norms of orthonormal polynomials for Erdös weights , 1997 .

[15]  The Lebesgue Function and Lebesgue Constant of Lagrange Interpolation for Erdoős Weights , 1998 .