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Proceedings of the American Mathematical Society

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

 

 

On zero sets for the ball algebra


Author: H. Alexander
Journal: Proc. Amer. Math. Soc. 86 (1982), 71-74
MSC: Primary 32A10; Secondary 32E25, 46J15
DOI: https://doi.org/10.1090/S0002-9939-1982-0663869-0
MathSciNet review: 663869
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Abstract: Rudin has constructed a function in the ball algebra in $ {{\mathbf{C}}^2}$ whose zero set has infinite volume and has asked if such functions exist in $ {{\mathbf{C}}^n}$. Using some recent work of Ryll and Wojtaszczyk on homogeneous polynomials we shall extend Rudin's proof to $ {{\mathbf{C}}^n}$ for arbitrary $ n$.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0663869-0
Article copyright: © Copyright 1982 American Mathematical Society