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Functions in N+ with the positive real parts on the boundary

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83632

Title: Functions in N+ with the positive real parts on the boundary
Authors: Nakazi, T. Browse this author
Keywords: Hardy space
exposed point
extremal problem
existence of solutions
Smirnov class
outer function
positive real part
Issue Date: 1-Jul-2000
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 486
Start Page: 1
End Page: 21
Abstract: An essentially bounded function</> on the unit circle gives a continuous linear functional T,p on the Hardy space H1 • p( </>) denotes a set of all complex numbers s such that there exists at least one function which attains the norm of T¢,-s· In a previous paper, we showed that C\p(</>) is empty or an open disc. Unfortunately we did not know when p( </>) is open or closed. In this paper, we study when p( </>) is open or closed. Moreover the functions in the Smirnov class N+ whose real parts are nonnegative on the unit circle are described and studied. Then we give new characterizations of exposed points in the unit ball of H1 and we determine when th􀀕 sum of two inner functions is outer. As an result, we can describe all functions which have their Denjoy-Wolff points on the unit circle.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69236
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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