Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607554 | Journal of Approximation Theory | 2010 | 17 Pages |
Abstract
We investigate the coefficients of Hermite-Fejér interpolation polynomials based at zeros of orthogonal polynomials with respect to exponential-type weights. First, we obtain the modified Markov-Bernstein inequalities with respect to wâF(Lip12). Then using the modified Markov-Bernstein inequalities, we estimate the value of |pn(r)(wÏ2,x)/pnâ²(wÏ2,x)| for r=1,2,⦠at zeros of pn(wÏ2;x) and we apply this to estimate the coefficients of Hermite-Fejér interpolation polynomials. Here, pn(wÏ2,x) denotes the nth orthogonal polynomial with respect to an exponential-type weight wÏ(x)=|x|Ïw(x), xâR, Ï>â1/2.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
H.S. Jung, R. Sakai,