An extreme point in $H^{\infty }(U^{2})$
HTML articles powered by AMS MathViewer
- by Nathaniel R. Riesenberg PDF
- Proc. Amer. Math. Soc. 76 (1979), 129-130 Request permission
Abstract:
In this paper an example of a function $f \in {H^\infty }({U^2})$ with ${\left \| f \right \|_\infty } = 1$ and \[ \int _{{T^2}} {\log (1 - |{f^ \ast }(z)|)dm > - \infty ,\quad z \in {T^2}} ,\] yet f is an extreme point in the unit ball of ${H^\infty }$, is given. For functions $f \in {H^\infty }({U^1})$ that \[ \int _T {\log (1 - |{f^ \ast }(z)|)dm = - \infty ,\quad z \in T,} \] is both necessary and sufficient for f to be an extreme point in ${H^\infty }$.References
- 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, Inner functions in polydiscs, Bull. Amer. Math. Soc. 73 (1967), 369–372. MR 209516, DOI 10.1090/S0002-9904-1967-11755-5
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 76 (1979), 129-130
- MSC: Primary 32A35; Secondary 30D55, 46J15
- DOI: https://doi.org/10.1090/S0002-9939-1979-0534402-9
- MathSciNet review: 534402