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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Polynomial hulls with convex sections and interpolating spaces

Author: Zbigniew Slodkowski
Journal: Proc. Amer. Math. Soc. 96 (1986), 255-260
MSC: Primary 32E20; Secondary 46E99, 46M35
MathSciNet review: 818455
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Abstract: Assume that $ L \subset \partial D \times {{\mathbf{C}}^m}$ is compact and has convex vertical sections. Denote by $ K$ its polynomially convex hull. It is shown that $ K\backslash \partial D \times {{\mathbf{C}}^m}$, if nonempty, can be covered by graphs of analytic functions $ f:D \to {{\mathbf{C}}^m}$. The proof is based on complex interpolation theory for families of finite-dimensional normed spaces.

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Article copyright: © Copyright 1986 American Mathematical Society