caa a22 4500 388024194 CHVBK 20180307124932.0 cr unu---uuuuu 161130e199810 xx s 000 0 eng 10.1017/S0013091500019829 doi S0013091500019829 pii (NATIONALLICENCE)cambridge-10.1017/S0013091500019829 Hasson Maurice Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, U.S.A., E-mail: hasson@math.rutgers.edu Concentration of the error between a function and its polynomial of best uniform approximation [Elektronische Daten] [Maurice Hasson] Let f be a continuous real valued function defined on [−1, 1] and let En(f) denote the degree of best uniform approximation to f by algebraic polynomial of degree at most n. The supremum norm on [a, b] is denoted by .[a, b] and the polynomial of degree n of best uniform approximation is denoted by Pn. We find a class of functions f such that there exists a fixed a (−1, 1) with the following property for some positive constants C and N independent of n. Moreover the sequence is optimal in the sense that if is replaced by then the above inequality need not hold no matter how small C > 0 is chosen. We also find another, more general class a functions f for which infinitely often. Copyright © Edinburgh Mathematical Society 1998 Proceedings of the Edinburgh Mathematical Society Cambridge University Press 41/3(1998-10), 447-463 0013-0915 41:3<447 1998 41 PEM https://doi.org/10.1017/S0013091500019829 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0013091500019829 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hasson Maurice Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, U.S.A., E-mail: hasson@math.rutgers.edu NATIONALLICENCE 773 0- Proceedings of the Edinburgh Mathematical Society Cambridge University Press 41/3(1998-10), 447-463 0013-0915 41:3<447 1998 41 PEM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge