DE PAEPE'S DISC HAS NONTRIVIAL POLYNOMIAL HULL

Abstract

The topological disc (De Paepe's) P = { ( z 2 , z ¯ 2 + z ¯ 3 ) : | z | ⩽ 1 } ⊂ C 2 is shown here to have non-trivial polynomially convex hull. In fact, the authors show that this holds for all discs of the form X = { ( z 2 , f ( z ¯ ) ) : | z | ⩽ r } , where f is holomorphic on |z|⩽r, and f(z=z2+a3z3+…, with all coefficients an real, and at least one a2n+1 ≠ 0. 2000 Mathematics Subject Classification 32E20.