单位圆盘上解析Hilbert空间的极大不变子空间

《单位圆盘上解析Hilbert空间的极大不变子空间》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、硕士学位论文论文题目单位圆盘上解析Hilbert空间的极大不变子空间研究生姓名张静指导教师姓名卫淑云（教授）专业名称基础数学研究方向泛函分析论文提交日期2014年4月üþ)ÛHilbert˜m4ŒØCf˜mÁ‡Á‡©ïÄüþS)ÛHilbert˜m9Dirichlet˜m4ŒØCf˜m¯K.Äky²S)ÛHilbert˜m4ŒØCf˜m•I•1.Ùgé˜aS)ÛHilbert˜m•I•1ØCf˜mM,y²M4ŒØCf˜mNäk/ªN=(z)M.•éDirichlet˜m4ŒØCf˜m‰Ñ•x,=M•D4ŒØCf˜m…=M=[

2、z]=(z)D,Ù¥2D.'…cµS)ÛHilbert˜m;k•{‘;•I;4ŒØCf˜m;Dirichlet˜m.Šö:Ü·•“:¥Ô(Ç)IAbstractMaximalinvariantsubspacesforHilbertspacesofanalyticfunctionsMaximalinvariantsubspacesforHilbertspacesofanalyticfunctionsovertheunitdiscAbstractInthispaper,wefocusonmaximalinvariantsubspacesforo

3、rderedanalyticHilbertspacesovertheunitdiscandtheDirichletspace.Firstly,weshowthatmaximalin-variantsubspacesinorderedanalyticHilbertspaceshaveindexone.Secondly,weobtainthatifMisaninvariantsubspaceofaclassoforderedanalyticHilbertspacesanddimM•zM=1,theneverymaximalinvariantsubspaceofM

4、isoftheformN=(z)M.Finally,wegiveacompletedescriptionformaximalinvariantsub-spacesoftheDirichletspace.Thatis,aninvariantsubspaceMoftheDirichletspaceismaximalifandonlyifMisoftheformM=[z]=(z)D,2D.Keywords:orderedanalyticHilbertspaces;nitecodimension;index;maximalin-variantsubs

5、pace;Dirichletspace.WrittenbyZhangJingSupervisedbyProf.WeiShuyunII8¹1˜ÙÚó.............................................................11ÙS)ÛHilbert˜m4ŒØCf˜m................................31nÙDirichlet˜m4ŒØCf˜m...................................11ë•©z............................

6、...................................15—...................................................................17üþ)ÛHilbert˜m4ŒØCf˜m1˜ÙÚó1˜ÙÚóH•Œ©Hilbert˜m§T•Hþk.‚5Žf,M´H4f˜m.eTMM,K¡M´TØCf˜m.ØCf˜m†Žf(—ƒƒ',ØCf˜m´ŽfnØ•‡ïÄ‘K,8c®´LïĤJ.ͶØCf˜m¯K•:¯KA:Œ©Hilbert˜mþz‡k.‚5Žf´Ä•

7、3š²…ØCf˜m?)ÛHilbert˜mØCf˜mþ•Ùþ¦{ŽfMzØCf˜m.ÃXHardy˜m!Bergman˜m!Dirichlet˜m²;¼ê˜mØCf˜mnØ®²´LïĤJ.²;Beurling½nL²:Hardy˜mš"ØCf˜mþ´d˜‡S¼ê)¤…•I•1[16].S.Richter,C.Sundberg3[17]¥y²Dirichlet˜mØCf˜m´d¦f)¤;S.Richter,A.Shields3[11]¥y²Dirichlet˜mØCf˜m•I•1.Bergman˜mØCf˜mnØ3L›cp•

8、•‡?Ð,ÙI“5¤Jƒ˜´A.Aleman,S