Canonical products and the weights exp(−¦x¦α), α > 1, with applications

AbstractLet α > 1. For each positive integer n, a polynomial Sn(x) of degree ⩽ n is constructed such that Sn(x) ~ exp(−¦x¦α), ¦x¦ ⩽ Cn1α, where C > 0 is independent of n. These polynomials enable one to estimate Christoffel functions and prove Lp Markov-Bernstein inequalities for all 0 < p ⩽ ∞, and for all the weights exp(− ¦x¦α), α > 1. In particular, the gap 1 < α < 2 in Feud's approximation theory can be filled, and one can prove Lp Markov-Bernstein inequalities for 0 < p < 1