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An argument of a function in H1/2

Part of: Spaces and algebras of analytic functions

Published online by Cambridge University Press:  23 February 2012

Takahiko Nakazi  and
Takanori Yamamoto
Takahiko Nakazi
Affiliation:
School of Economics, Hokusei Gakuen University, Sapporo 004-8631, Japan (z00547@hokusei.ac.jp)
Takanori Yamamoto
Affiliation:
Department of Mathematics, Hokkai-Gakuen University, Sapporo 062-8605, Japan (yamamoto@elsa.hokkai-s-u.ac.jp)
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Abstract

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Let H1/2 be the Hardy space on the open unit disc. For two non-zero functions f and g in H1/2, we study the relation between f and g when f/g ≥ 0 a.e. on ∂D. Then we generalize a theorem of Neuwirth and Newman and Helson and Sarason with a simple proof.

Keywords

Hardy spaceargumentboundary value

MSC classification

Secondary: 30H10: Hardy spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 2 , June 2012 , pp. 507 - 511
Copyright
Copyright © Edinburgh Mathematical Society 2012

References

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5.Neuwirth, J. and Newman, D. J., Positive H 1/2 functions are constants, Proc. Am. Math. Soc. 18 (1967), 958.Google Scholar