Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  808.41006
Autor:  Erdös, Paul; Newman, D.J.; Knappenberger, J.
Title:  Forcing two sums simultaneously. (In English)
Source:  Knopp, Marvin (ed.) et al., A tribute to Emil Grosswald: number theory and related analysis. Providence, RI: American Mathematical Society, Contemp. Math. 143, 321-328 (1993).
Review:  The second author and T. J. Rivlin [Analysis 3, 355-367 (1983; Zbl 575.41006)] sought an optimal rational interpolation process that was Féjer-stable at all sets of nodes \bf x: (x0,..., xn). They established the proposition that, if \bf x in (0,n] and n \geq 2, then

maxy in (0,n] \left{[sumnk = 1 1/|y-xk|] / [sumnk = 1 1/(y- xk)2]\right} \geq (log n)/300.

In this paper, the authors strengthen this result by showing that when n is large, there is a point y in [0,n] where the numerator exceeds a constant times log n and the denominator is bounded.
Reviewer:  P.A.McCoy (Annapolis)
Classif.:  * 41A17 Inequalities in approximation
                   26D05 Inequalities for trigonometric functions and polynomials
                   26D15 Inequalities for sums, series and integrals of real functions
Keywords:  Fejer-stable interpolation; asymptotic lower bound
Citations:  Zbl 575.41006

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