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Inner functions on the polydisc

Author: S. H. Kon
Journal: Proc. Amer. Math. Soc. 73 (1979), 338-340
MSC: Primary 46J15; Secondary 32A35
MathSciNet review: 518515
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Abstract: It is shown that the inner functions on the polydisc, unlike the classical case of the unit disc, fail to separate the points of the maximal ideal space of $ {H^\infty }({U^n})$. From this we deduce that the inner functions generate a proper closed subalgebra of $ {H^\infty }({U^n})$.

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  • [1] R. G. Douglas and W. Rudin, Approximation by inner functions, Pacific J. Math. 31 (1969), 313-320. MR 0254606 (40:7814)
  • [2] K. Hoffman, Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR 0133008 (24:A2844)
  • [3] S. H. Kon, Inner functions and the maximal ideal space of $ {L^\infty }({T^n})$, J. Austral. Math. Soc. (to appear).
  • [4] D. E. Marshall, Blaschkeproducts generate $ {H^\infty }$, Bull. Amer. Math. Soc. 82 (1976), 494-496. MR 0402054 (53:5877)
  • [5] M. Range, A small boundary for $ {H^\infty }$ on the polydisc, Proc. Amer. Math. Soc. 32 (1972), 253-255. MR 0290115 (44:7300)

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Keywords: Inner functions, bounded analytic functions, polydisc, $ {H^\infty }({U^n})$, maximal ideal space, Shilov boundary, $ {L^\infty }({T^n})$, separate points
Article copyright: © Copyright 1979 American Mathematical Society

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