Forward and converse theorems of polynomial approximation for exponential weights on [-1, 1] .1.

[摘要] We consider exponential weights of the form w: = e(-Q) on (-1, 1) where Q(x) is even and grows faster than (1 - x(2))(-delta) near +/-1, some delta > 0. For example, we can take Q(x): = exp(k)((1-x(2))(-alpha)), k greater than or equal to 0, alpha > 0, where exp(k) denotes kth iterated exponential exp(0)(x) = x. We prove Jackson theorems in weighted L-p spaces with norm \\fw\\(Lp(-1, 1)) for all 0 < p less than or equal to infinity. In part II of this paper, we shall prove matching converse theorems. (C) 1997 Academic Press.

[发布日期] 1997-10-01