1、陜西師范大學(xué)碩士學(xué)位論文多重正交小波和多尺度分析姓名：成立花申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：曹懷信20050401OrthogonalMultiwaveletandmultiresolutionanalysisChengLiHuaAbstractWaveletanalysisisanapplicateddepartmentbeganin80thyearsof20centurywhichisallimprovementandde

2、velepmentoftraditionalFourieranal—ysisandiswidelyusedinareas，suchascompressionfigure，signalprocessing，fractalandsoonMultiwaveletsisannewlydepartmentrecentlysinceithassomeadva41ragedifferentfromwaveletBasedonsomeexistingp

3、apem，wemainlycharacterizeorthogonalmultiwaveletsanditsconstruction，equivalentconditionsofRieszmultiwaveletassociatedwithmultiresolutionanalysis，characterisationofapairofmultiwaveletsaesotiatedwithmultiresolutionanalysisT

4、histhesisconsistsoffourchaptersThemainresultsareasfollowsInchapter1，weconcentrate0nthepreliminariesincludingsomenotationsanddefinitions，suchaSBesselsequence，frameIPdeszbasis，orthogonalwaveletandRieszwaveletandSOon，thengi

5、vesomewellknowntheoremsInchapter2，firstofa11wecharacterizesubspaceVoofmu】tiresultionanalysi8吩)一∞cobasedoninvariantsubspaceSubsequentlyweconsidertheequivalentconditionsamongorthogonalmultiwavelet皿一(妒l，妒2，t一，佴)7，subspace，b

6、asisanddimensionofsubspace，propertiesoffilterfunctionmatrixP∞)oxede眥withLastlywegivesomeconditionsofnfunctiontobeanscalingfunctionInchapter3，havingstudiedrelationbetweenfilterfunctionmatricesassociatedwithFouriertransfor

7、mofscal堍function圣=(咖l，妒2，一，Cr)randmultiwavelet皿=(母l，也，，“)7，wediscussrelationshipOnbasisofsubspacesVo，Ⅵandfilterfunctionmatrix；Inaddition，weprovetheexistenceoforthogonalmultiwaveletandCOnStructitInchapter4，weconverttothep

8、ropertiesofRieszmultiwaveletandbringoutasetofequivalentconditionsamongRieszmultiwaveletsmscalingfunction西andlow，highfilterfunctionmatrix；Havinganalylizedtheconditionsoftwofunctiontransformedofmultiwaveletassociatedwithmu

9、ltisolutionanalysis，dimensionoffunctionmatrixM∞)andmultiwavelet皿FinallyweprovethemainresultofapairofbiorthogonalmultiwaveletsassociatedwithmultisolutionanalysisKeywordsOrthogonalmultiwavelet；multiresolutionanalysis；ortho