On the constructive theory of functions I.

Szüsz, P. and Turán, P. (1964) On the constructive theory of functions I. A MAGYAR TUDOMÁNYOS AKADÉMIA MATEMATIKAI KUTATÓ INTÉZETÉNEK KÖZLEMÉNYEI, 9 (3). pp. 495-502.

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Abstract

In a recent very interesting note 1 D. J. N EWMA N mad e the observation tha t the | x |-function, which plays an essential rôle in th e theory of polynomial-approximation shows an unexpected behavior when turning to approximation by rational functions. While it is well-known tha t for suitable positive numerical cx and c2 (and later c3) an d for all n Lt I ther e exists a polynomial2 л%(х) such that for — 1 ^ x ^ 1

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