Christoffel functions and orthogonal polynomials for exponential weights on [-1,1]

1994 ◽  
Vol 111 (535) ◽  
pp. 0-0 ◽  
Author(s):  
A. L. Levin ◽  
D. S. Lubinsky
Keyword(s):  
Orthogonal Polynomials ◽  
Exponential Weights ◽  
Christoffel Functions

scholarly journals Orthogonal polynomials for exponential weights x2α(1 – x2)2ρe–2Q(x) on [0, 1)

2020 ◽  
Vol 18 (1) ◽  
pp. 138-149
Author(s):  
Rong Liu
Keyword(s):  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Lagrange Interpolation ◽  
Restricted Range ◽  
Exponential Weights ◽  
Christoffel Functions

Abstract Let Wα,ρ = xα(1 – x2)ρe–Q(x), where α > – $\begin{array}{} \displaystyle \frac12 \end{array}$ and Q is continuous and increasing on [0, 1), with limit ∞ at 1. This paper deals with orthogonal polynomials for the weights $\begin{array}{} \displaystyle W^2_{\alpha, \rho} \end{array}$ and gives bounds on orthogonal polynomials, zeros, Christoffel functions and Markov inequalities. In addition, estimates of fundamental polynomials of Lagrange interpolation at the zeros of the orthogonal polynomial and restricted range inequalities are obtained.

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

1998 ◽  
Vol 50 (6) ◽  
pp. 1273-1297 ◽  
Author(s):  
D. S. Lubinsky
Keyword(s):  
Orthogonal Polynomials ◽  
Lagrange Interpolation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Exponential Weights ◽  
Mean Convergence ◽  
Zeros Of Orthogonal Polynomials ◽  
Necessary And Sufficient

AbstractWe obtain necessary and sufficient conditions for mean convergence of Lagrange interpolation at zeros of orthogonal polynomials for weights on [-1, 1], such asw(x) = exp(-(1 - x2)-α), α > 0orw(x) = exp(-expk(1 - x2)-α), k≥1, α > 0,where expk = exp(exp(. . . exp( ) . . .)) denotes the k-th iterated exponential.

scholarly journals Asymptotics for Sobolev Orthogonal Polynomials for Exponential Weights

2004 ◽  
Vol 22 (3) ◽  
pp. 309-346 ◽  
Author(s):  
J. S. Geronimo ◽  
D. S. Lubinsky ◽  
F. Marcellan
Keyword(s):  
Orthogonal Polynomials ◽  
Exponential Weights ◽  
Sobolev Orthogonal Polynomials
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