Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  098.27102
Autor:  Erdös, Pál; Turán, Pál
Title:  An extremal problem in the theory of interpolation. (In English)
Source:  Acta Math. Acad. Sci. Hung. 12, 221-234 (1961).
Review:  In connessione con il problema relativo alla convergenza delle successioni di polinomi interpolanti una funzione continua, gli AA. dimostrano: se A è una matrice triangolare:

A = \pmatrix x1,1
x1,n, x2,n, ···, xn,n
··· \endpmatrix,   1 \geq x1,n \geq x2,n \geq ··· \geq xn,n \geq -1,

\omegan(x) = prodj = 1n (x-xj,n), lj,n = {\omegan(x) \over \omegan'(xj,n (x-xj,n)}, hj,n = {[\omegan(x)]2 \over [\omega'n(xj,n]2 (x-xj,n)} esistono allora due costanti positive c1 e c2 tali che:

max-1 \leq x \leq 1 sumj = 1n |hj,n(x)| \geq {2 \over \pi n} (log n -c1 log log n),

max-1 \leq x \leq 1 sumj = 1n |lj,n(x)| \geq {2 \over \pi} log n - c2 log log n.

Reviewer:  G.Sansone
Classif.:  * 41A05 Interpolation
Index Words:  approximation and series expansion

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