帶平方根的邊值問題及雙解析函數(shù)的Riemann邊值逆問題.pdf

1、分類號Q!Z5：8密級UDC碩士學位論文帶平方根的邊值問題及雙解析函數(shù)的Riemann邊值逆問題THEBoUNDAR：yVALUBPRoBLEMSWITHSQUARERooTSANDTHEINVERSE托IEMANNBoUNDAR：yVALUEPRoB毛EMSFoRBIANALVTICFUNeTIoNS學科專業(yè)指導教師史西專應用數(shù)學黃新民教授論文答辯日期～!!墮生!旦!!旦學位授予日期答辯蠶是會主席熊壤玲教授論文評閱人熊縫堡塑堡奎造塑型

2、塑堡THEBoUNDARYVALUEPRoBLEMSWITHSQUARER00TSANDTHEINVERSERIEMANNBoUNDARYVALUEPROBLEMSFoRBIANALyTICFUNeTIONSABSTRACTBoundaryValuepro磋emfor8壬lalytcfunetionsi8o矬e。fthemostimportgntbranchesinthetheoryofcomplexfullctioIl8Theyare

3、notonlyimportantinthe—ofybut8|80e)【ten8iveiIlap壬)lieationNonlinearRiemannboundaryv8l船eprobl￡瞄andnonIine盯Hilbertboundaryvalueproblemswillbcstudiedinthispaper，becausetheyh批beenresearched8eldomT沁re8earchofbiaI“yticfIl工lctio

4、ns，poly鞠丑JyticfunctionsandinversefHemannboundaryvalueproblemsi8animportantquestionfordiscussioninrccentlyycarsThisp印erwillalsodiscussakindofinverseIUemannbo佳ndary越ucproblemsforbianalyticfunet主。璐Firstly，thesolutionofa姑ndo

5、fRiemanⅡbounda。yValueproblemwithsquar。rootsonmopensmoothlyaTcisconsideredByan8lyzing瓶e8truetureoftheunkn。wnfunction，theproblemistransformedintoatypic“memannbound甜yvalueproblemon8nopen8rc，anditss越utionsaswellastheconditio

6、粥ofi據(jù)solvabiIit，faregivenaccordingtotheknowntheo彤Second墳Hi瑪ertboHnd8ryV越ueproblemwith8∞8糟footsinthe即perh函f_planeisdi8cussedA8abo^^e，byanalyzingthestructureoftheunkn。MⅡfunction，theproblemi8transfo艄edintoatypicalHilbertbou

7、ndaryv甜ueproble】丑intheupperhalfplaneThentheproblemi8furtherequivalenttoal(indofRiemannb。undary訓ueproblemontherealaxi8bye)(ten8ionofsymmetrywithrespecttotherealaxiSAsaresult，weestabli8hthetheoreⅡls。fitssolVabilityaccordiⅡ

8、gtothekndWh穗eoryFinally’Aclas8ofinVersememannboundaryvalucprobl鋤forbianalyticfunctionsoⅡthere甜lxi8isprop()8ed。By磚白ninatingpararneticunkncwnftmctions齜ldusingthenotation0fmatrixformwhichwillbegeneralizedeasily，thepmblemi8t