Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T16:32:56.114Z Has data issue: false hasContentIssue false

DE PAEPE'S DISC HAS NONTRIVIAL POLYNOMIAL HULL

Published online by Cambridge University Press:  24 March 2003

A. G. O'FARRELL
Affiliation:
Department of Mathematics, National University of Ireland, Maynooth, Co. Kildare, [email protected]@maths.may.ie
M. A. SANABRIA-GARCÍA
Affiliation:
Department of Mathematics, National University of Ireland, Maynooth, Co. Kildare, [email protected]@maths.may.ie
Get access

Abstract

The topological disc (De Paepe's) \[ P=\{(z^2,\bar{z}^2+\bar{z}^3):|z|\le 1\}\subset {\bb C}^2 \]

is shown here to have non-trivial polynomially convex hull. In fact, the authors show that this holds for all discs of the form $X=\{(z^2,f(\bar{z})):|z|\le r\}$ , where $f$ is holomorphic on $|z|\le r$ , and $f(z)=z^2+a_3z^3+\ldots$ , with all coefficients $a_n$ real, and at least one $a_{2n+1}\ne 0$ .

Type
NOTES AND PAPERS
Copyright
© The London Mathematical Society 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)