复平面上解析Banach空间拟不变子空间的指标

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1、硕士学位论文论文题目复平面上解析Banach空间拟不变子空间的指标研究生姓名罗晴指导教师姓名卫淑云专业名称基础数学研究方向泛函分析论文提交日期2013-04€²ŒÆÆØ©ÕM5(²9¦^Ç(²ÆØ©ÕM5(²LïĤJ,•Ø¹•¼€²ŒÆ½Ù§˜ÅÆyÖ¦^Lá.é©ïÄŠÑ•‡z‡<Ú8N,þ®3©¥±²(•ªI².<«ú(²{ÆI?.ïÄ)¶:Fϵ€²ŒÆÆØ©¦^Ç(²

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4、^"‘˜?ê•{‰ÑE²¡þ)ÛBanach˜m•3?¿•I½½n,Š•A^,·‚y²Fock.˜mZp1pjzj2F(C)=ff2Hol(C):jf(z)jedA(z)<+1gC†Hilbert˜mZ12jzjH=ff2Hol(C):jf(z)jedA(z)<+1gCäk?¿•I.'…cµ•I,)Û,E²¡,[ØCf˜m.Šö:Ûš•“:¥Ô(Ç)IAbstractTheindexofquasi-invariantsubspacesinBanachspacesTheindexofquasi-invariantsubsp

5、acesinBanachspacesofanalyticfunctionsoverthecomplexplaneAbstractInthispaper,welistgeneralconditionsonBanachspacesofanalyticfunctionsoverthecomplexplaneimplyingtheexistenceofquasi-invariantsubspacesofarbitraryindex,anduselacunarypowerseriestoproveitscorrectness.Asapplication,weal

6、sodescribethattheFockspaceZp1pjzj2F(C)=ff2Hol(C):jf(z)jedA(z)<+1gCandHilbertspaceZ12jzjH=ff2Hol(C):jf(z)jedA(z)<+1gCcontainquasi-invariantsubspacesofarbitraryindex.Keywords:index,analytic,complexplane,quasi-invariantsubspace.WrittenbyLuoQingSupervisedbyProf.WeiShuyunII8¹1˜ÙÚ

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8、.....................27—...................................................................29E²¡þ)ÛBanach˜m[ØCf˜m•I1˜ÙÚóÚO1˜ÙÚóÚORHardy˜mH2´düþ÷vff:limjf(rei)j2d<+1g)Û¼r!1jzj=rê

9、¤Hilbert˜m.ŠâBeurling½n,éHardy˜mz‡š"ØCf˜mM,Ñ•3S¼ê,¦M=H2.ldim(M=zM)=1,=Hardy˜mz‡š"ØCf˜mM

10、•IÑ•1[1].RDirichlet˜m´düþ÷vff:1jf0(z)j2dm(z)<