A small boundary for $H^{\infty }$ on the polydisc
HTML articles powered by AMS MathViewer
- by R. Michael Range PDF
- Proc. Amer. Math. Soc. 32 (1972), 253-255 Request permission
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
- Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
Additional Information
- © Copyright 1972 American Mathematical Society
- 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