Inner functions on the polydisc
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- by S. H. Kon PDF
- Proc. Amer. Math. Soc. 73 (1979), 338-340 Request permission
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 ${H^\infty }({U^n})$.References
- R. G. Douglas and Walter Rudin, Approximation by inner functions, Pacific J. Math. 31 (1969), 313–320. MR 254606
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008 S. H. Kon, Inner functions and the maximal ideal space of ${L^\infty }({T^n})$, J. Austral. Math. Soc. (to appear).
- Donald E. Marshall, Blaschke products generate $H^{\infty }$, Bull. Amer. Math. Soc. 82 (1976), no. 3, 494–496. MR 402054, DOI 10.1090/S0002-9904-1976-14071-2
- R. Michael Range, A small boundary for $H^{\infty }$ on the polydisc, Proc. Amer. Math. Soc. 32 (1972), 253–255. MR 290115, DOI 10.1090/S0002-9939-1972-0290115-6
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 338-340
- MSC: Primary 46J15; Secondary 32A35
- DOI: https://doi.org/10.1090/S0002-9939-1979-0518515-3
- MathSciNet review: 518515