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A small boundary for $ H^{\infty }$ on the polydisc


Author: R. Michael Range
Journal: Proc. Amer. Math. Soc. 32 (1972), 253-255
MSC: Primary 46.55; Secondary 32.00
DOI: https://doi.org/10.1090/S0002-9939-1972-0290115-6
MathSciNet review: 0290115
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Abstract: Let $ {\Delta ^n}$ be the unit polydisc in $ {C^n}$ and let $ {T^n}$ be its distinguished boundary. It is shown that for $ n \geqq 2$ there is a nowhere dense subset of the maximal ideal space of $ {L^\infty }({T^n})$ which defines a closed boundary for $ {H^\infty }({\Delta ^n})$.


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

  • [1] T. W. Gamelin, Uniform algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. MR 0410387 (53:14137)
  • [2] K. Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Anal., Prentice-Hall, Englewood Cliffs, N.J., 1962. MR 24 #A2844. MR 0133008 (24:A2844)
  • [3] W. Rudin, Function theory in polydiscs, Benjamin, New York, 1969. MR 41 #501. MR 0255841 (41:501)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0290115-6
Keywords: Bounded holomorphic functions, polydisc, closed boundary, Shilov boundary
Article copyright: © Copyright 1972 American Mathematical Society

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