Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T00:33:05.829Z Has data issue: false hasContentIssue false
  • English
  • Français

Sum of two inner functions and exposed points in H1

Published online by Cambridge University Press:  20 January 2009

Takahiko Nakazi
Takahiko Nakazi
Affiliation:
Department of MathematicsFaculty of ScienceHokkaido UniversitySapporo 060Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If h is an outer function in H1 then it is shown that h = (q1 + q2)g where both q1 and q2 are inner functions with Im almost everywhere, and g is a strong outer function (equivalently, g/∥g∥1 is an exposed point of the unit ball of H1). If q1 + q2 is nonconstant then such an h is not strongly outer. Moreover a sum of two inner functions is studied.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 3 , October 1992 , pp. 349 - 357
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

1.Buerling, A., On two problems concerning linear transformations in Hubert space, Acta Math. 81 (1949), 239–255.CrossRefGoogle Scholar
2.De Leeuw, K. and Rudin, W., Extreme points and extreme problems in H 1, Pacific J. Math. 8 (1958), 467–485.CrossRefGoogle Scholar
3.Garnett, J., Bounded Analytic Functions (Academic Press, New York, N.Y., 1981).Google Scholar
4.Hayashi, E., The solution sets of extremal problems in H 1, Proc. Amer. Math. Soc. 93 (1985), 690–696.Google Scholar
5.Hayashi, E., The kernel of a Toeplitz operator, Integral E q,. Operator Th. 9 (1986), 589–591.Google Scholar
6.Helson, H., Large analytic functions, Oper. Theory: Adv. Appl. 43 (1989), 209–216.Google Scholar
7.Helson, H., Large analytic functions II, in Analysis and Partial Differential Equations (Sadosky, C., ed., Marcel Dekker, Basel, 1990).Google Scholar
8.Nakazi, T., Exposed points and extremal problems in H 1, J. Funct. Anal 53 (1983), 224–230.CrossRefGoogle Scholar