On zero sets for the ball algebra
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- by H. Alexander PDF
- Proc. Amer. Math. Soc. 86 (1982), 71-74 Request permission
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 $n$.References
- Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
- J. Ryll and P. Wojtaszczyk, On homogeneous polynomials on a complex ball, Trans. Amer. Math. Soc. 276 (1983), no. 1, 107–116. MR 684495, DOI 10.1090/S0002-9947-1983-0684495-9
- P. Wojtaszczyk, On functions in the ball algebra, Proc. Amer. Math. Soc. 85 (1982), no. 2, 184–186. MR 652438, DOI 10.1090/S0002-9939-1982-0652438-4
Additional Information
- © Copyright 1982 American Mathematical Society
- 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