Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  817.41006
Autor:  Erdös, Paul; Szabados, J.; Varma, A.K.; Vértesi, P.
Title:  On an interpolation theoretical extremal problem. (In English)
Source:  Stud. Sci. Math. Hung. 29, No.1-2, 55-60 (1994).
Review:  Let w(x) = (1-x)\alpha (1+x)\beta, |x| < 1, \gamma = max(\alpha,\beta) > -1, be the Jacobi weight. The authors prove the evaluations:

int+1-1 w(x) sumnk = 1 \ell2sk(x) dx \geq 1/s int+1-1 w(x) dx- O({log2 n\over n}) if \gamma > - ½;
-O({log3n\over n}), if \gamma = - ½;  - O({log6 n\over n}), if -1 < \gamma < -1,2,

for any system of nodes 1 \geq x1 > x2 > ··· > xn \geq -1. The constants represented by ``O'' depend only on s. Here \ellk(x) = prodni = 1, i\ne k (x- xi)/(xk- xi) are the fundamental interpolation polynomials associated to the given system of nodes.
Reviewer:  C.Mustata (Cluj-Napoca)
Classif.:  * 41A05 Interpolation
                   41A10 Approximation by polynomials
                   41A44 Best constants
Keywords:  interpolation

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