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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