兩種再生核的作用.pdf

1、哈爾濱理工大學(xué)碩士學(xué)位論文兩種再生核的作用姓名：徐延新申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：鄧彩霞20090301哈爾濱理工大學(xué)理學(xué)碩十學(xué)位論文TwoApplicationsofReproducingKernelsAbstractTheReproducingKernelSpaceiSmoreidealspaceframeintheresearchofnumericalanalysisItiSgoodnumberperformance

2、thedintlieinthatthereexistsafunctionsuchthatitexpressthereproducibilityforfixofvariantwithcorrespondofthefunctionbyinteriorproductinthespaceHencethebasicoperationinthenumericalanalysishasasuccessiveexpress，justbecausethi

3、spropertythatholdsdiscreteproblemexpressedsuccessive，maketheoptimizationofeachkindofnumberproblemmakepossibleSostudythepropertiesofreproducingkernelseemtobehighlyimportanceNowtheBergrnankernelhasbeenwidelyusedincommunica

4、tiontheoryimageprocessing，geologicalexploration，andmeasurementetcThepropertiesofBergmankernelshavealreadybeenstudiedbyscholarsandtheresultpileuponeafteranotherWeaimatthespecialreproducingkernelanalyticBergmankernelandhar

5、monicBergmankernelwhichbasedonthetheoryofreproducingkernelfunctionSomenewpropertiesareestablishedontheunitdiskbyvirtueofthedefinitionoftworeproducingkernelfunctionsThesepropertiesareholdforanalyticBergmankernelatsomepoin

6、tsoftheunitdisk，forharmonicBergmankerneljustholdatsomepointsontherealaxisoftheunitdiskSothepropertyofanalyticBergrnankernelisbetterthantheharmonicBergmankernelattheunitdiskThesepropertieshaveimportantmeaningforfurtherres

7、earchofreproducingkernelBergmanspaceonunitballandalsoprovidetheoreticalfoundationstotheengineerapplicationThemultiwaveletsamplingtheoremfromWalter’SwaveletsamplingtheorembyreproducingkernelisgeneralizedWalterextendedthec

8、lassicalShannonsamplingtheoremtosomewaveletsubspacesWegeneralizethesamplingtheoremformultiwaveletsubspacestomulti—waveletsubspaceswithatwoscalingfunctionofMultiResolutionAnalysis(MRA)basedonreproducingkernelHilbertspaceT