ASYMPTOTICS FOR LP EXTREMAL POLYNOMIALS ON THE UNIT-CIRCLE

Let p > 1, and dμ a positive finite Borel measure on the unit circle Γ: = {z ε{lunate} C: |z| = 1}. Define the monic polynomial φn, p(z)=zn+...ε{lunate}Pn >(the set of polynomials of degree at most n) satisfying ∫ G{cyrillic}|φn, p(z)|pPε{lunate}Pn-1inf ∫ G{cyrillic}|zn + P|p dμ. Under certain conditions on dμ, the asymptotics of φn, p(z) for z outside, on, or inside Γ are obtained (cf. Theorems 2.2 and 2.4). Zero distributions of φn, p are also discussed (cf. Theorems 3.1 and 3.2). © 1991.