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Finite dimensional solution sets of extremal problems in H1
Title:  Finite dimensional solution sets of extremal problems in H1 
Authors:  Inoue, Junji Browse this author  Nakazi, Takahiko Browse this author 
Issue Date:  Nov1992 
Publisher:  Department of Mathematics, Hokkaido University 
Journal Title:  Hokkaido University Preprint Series in Mathematics 
Volume:  171 
Start Page:  1 
End Page:  10 
Abstract:  For a nonzero 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 11 belongs to H1 then the dimension of < SIJl/f > , the linear span of S11111, is one. A simple example shows that even if 11 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 11 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 11 locally belongs to H1 on the unit circle except a finite set and that 11 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
