Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  060.05503
Autor:  Erdös, Pál; Szegö, Gábor
Title:  On a problem of I. Schur. (In English)
Source:  Ann. of Math., II. Ser. 43, 451-470 (1942); correction ibid. 74, 628 (1961).
Review:  Let Qn (x0) be a class of polynomials f(x) of degree n such that |f(x)| \leq 1 for -1 \leq x \leq 1 and f''(x0) = 0. The maximum mn· n2 of |f'(x0)| for -1 \leq x0 \leq 1 is attained if and only if x0 = ± 1, and f(x) satisfies the differential equation of Zolotareff. Furthermore, limn ––> oo mn and has the value 0.3124.
Reviewer:  E.Frank
Classif.:  * 26C05 Polynomials: analytic properties (real variables)
Index Words:  linear algebra, polynomials

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