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DE PAEPE'S DISC HAS NONTRIVIAL POLYNOMIAL HULL

Published online by Cambridge University Press:  24 March 2003

A. G. O'FARRELL  and
M. A. SANABRIA-GARCÍA
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
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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
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 4 , July 2002 , pp. 490 - 494
Copyright
© The London Mathematical Society 2002

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