Further Bounds and Applications

In this chapter, we obtain further upper (and lower) bounds on orthogonal polynomials and on their L _p norms. We also estimate fundamental polynomials of Lagrange interpolation, and spacing of zeros of orthogonal polynomials. We shall often need more than W∈F(lip1/2). Recall from Chapter 1 that we defined W∈F(lip1/2+) if both W∈F(lip1/2) and for each L>1, there exists C>0 and t0 such that $$ Q'\left( {{a_{{Lt}}}} \right)/Q'\left( {{a_{t}}} \right) \geqslant 1 + C,\left| t \right| \geqslant {t_{0}}. "$$