De Paepe’s disc has nontrivial polynomial hull

O'Farrell, A.G. and Sanabria-García, M.A (2002) De Paepe’s disc has nontrivial polynomial hull. Bulletin of the London Mathematical Society, 34 (4). pp. 490-494. ISSN 1469-2120

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Abstract. We show that the topological disc (De Paepe’s) P = {(z2, z¯2 +z¯3): |z| ≤ 1} ⊂ C2 has non-trivial polynomially-convex hull. In fact, we show that this holds for all discs of the form X = {(z2, 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.

Item Type: Article
Keywords: De Paepe’s disc; Topological disc; Polynomial hull; Approximation theory, Banach algebras; Spectral theory.
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1813
Identification Number: 10.1112/S0024609302001108
Depositing User: Prof. Anthony O'Farrell
Date Deposited: 27 Jan 2010 11:49
Journal or Publication Title: Bulletin of the London Mathematical Society
Publisher: Oxford University Press,
Refereed: Yes

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