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Finite dimensional solution sets of extremal problems in H1

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83315

Title: Finite dimensional solution sets of extremal problems in H1
Authors: Inoue, Junji Browse this author
Nakazi, Takahiko Browse this author
Issue Date: Nov-1992
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 171
Start Page: 1
End Page: 10
Abstract: For a non-zero function f in H1 , the classical Hardy space on the unit circle, put S11111 = {g E H1: Jlglli = 1, argl(eit) = argg(eit) a.e.t },then S1!1/ 1 is the set of extremal functions of a well known linear extremal problem in H1 . It is known and easy to see that if 1-1 belongs to H1 then the dimension of < SIJl/f > , the linear span of S11111, is one. A simple example shows that even if 1-1 belongs to HP for some p (0 < p < l), the dimension of < SIJI/ 1 > may be infinite. On the other hand, a sophisticated example ( will be shown in this paper) shows that even if 1-1 locally belongs to H1 on the unit circle except a finite set, the dimension of < S1!1/ 1 > may be infinite. In this paper it is shown that if I E H1 has the properties such that 1-1 locally belongs to H1 on the unit circle except a finite set and that 1-1 E HP for some p > 0, then the dimension of< SIJl/f > is finite.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/68917
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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