Weights on the real line that admit good relative polynomial approximation, with applications (Q1088082)

This paper extends the earlier results of the authors on canonical products and the weighted exponentials with applications. For large class of weights certain polynomials \(P_ n(x)\) are constructed satisfying suitable constraints. These are used to prove a number of theorems including \(L_ p\) Markov-Bernstein inequalities \((0<p\leq \infty)\) that are new for \(0<p<1\), except in special cases and lower bounds for Christoffel functions. Detailed proofs of theorems provide insight into several aspects of polynomial approximations.