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A note on monomials in several complex variables


Author: G. G. Weill
Journal: Proc. Amer. Math. Soc. 42 (1974), 541-542
MSC: Primary 32A15; Secondary 32E25
DOI: https://doi.org/10.1090/S0002-9939-1974-0328116-3
MathSciNet review: 0328116
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Abstract: Monomials in $ {C^n}$ are characterized in the polydisk algebra $ A({U^n})$ as functions whose modulus is constant on the distinguished boundary of $ {U^n}$ and whose zero set has an intersection with the diagonal of $ {U^n}$ consisting (at most) of the origin.


References [Enhancements On Off] (What's this?)

  • [1] R. Bojanic and W. Stoll, A characterization of monomials, Proc. Amer. Math. Soc. 13 (1962), 115-116. MR 25 #4129. MR 0140715 (25:4129)
  • [2] W. Rudin, Function theory in polydisks, Benjamin, New York, 1969. MR 41 #501. MR 0255841 (41:501)
  • [3] S. Bochner, Entire functions in several variables with constant absolute values on a circular uniqueness set, Proc. Amer. Math. Soc. 13 (1962), 117-120. MR 25 #4130. MR 0140716 (25:4130)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0328116-3
Keywords: Monomials, several complex variables, polydisk algebra
Article copyright: © Copyright 1974 American Mathematical Society

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