2023-06-06T08:44:51Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/689172022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Finite dimensional solution sets of extremal problems in H1Inoue, JunjiNakazi, Takahiko410For 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.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/68917info:doi/10.14943/83315https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/68917/1/pre171.pdfHokkaido University Preprint Series in Mathematics1711101992-11engpublisher