1、南京理工大學碩士學位論文有限樹圖上擴散算子的BgLevinson型定理姓名：劉鑫申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：黃振友20100623Abstract碩士論文AbstractWestudyboundaryvalueproblemsoncompactgraphswithoutcircles(ieonfinitetrees)forthequadraticdifferentialpenciloftheSchr6dingeropera

2、tor(iediffusionoperator)WeestablishthepropertiesofspectralcharacteristicsandinvestigatetheinversespectralproblemofuniquelydeterminingthepotentialsinthedifferentialequationsbyusingtheSO—calledDirichletNeumannmapinsteadoft

3、heTitchmarsh—Weylfunction(mfunction)fortheclassicalSturmLiouvilleoperators，andthenasallapplication，wediscusstheinversespectralproblemsoftheKlein—GordonequationsonthefinitetreegraphsWenotethattheobtainedresultsarenaturalg

4、eneralizationsofthewell—knownBorg—LevinsontheoremontheinversespectraltheoryfortheclassicalSturmLiouvilleoperatorsKeywords：Finitetreegraphs；Boundaryvalueproblems；Differentialpencils；Diffusionoperators；KleinGordonequation；