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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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Official URL: http://blms.oxfordjournals.org/cgi/reprint/34/4/49...
Abstract
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 |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/1813 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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