Springer.Wavelets.Approximation.&.Statistical.Applications.2002

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1、SeminaireParis-BerlinSeminarBerlin-ParisWavelets,ApproximationandStatisticalApplicationsWolfgangH•ardleGerardKerkyacharianDominiquePicardAlexanderTsybakovEinerstesErgebnisdesSeminarsBerlin-ParisUnpremierresultatduseminaireParis-BerlinW.H•ardleG.KerkyacharianHumboldt-Universit•atzuBerlinUniversit

2、eParisXWirtschaftswissenschaftlicheFakult•atURACNRS1321ModalxInstitutf•urStatistikundOkonometrie•200,av.delaRepubliqueSpandauerStrae192001NanterreCedexD10178BerlinFranceDeutschlandD.PicardA.B.TsybakovUniversiteParisVIIUniversiteParisVIUFRMathematiqueInstitutdeStatistiqueURACNRS1321URACNRS1321

3、2,PlaceJussieu4,pl.JussieuF75252Pariscedex5F75252ParisFranceFrance34Contents1Wavelets11.1Whatcanwaveletsoer?.....................11.2Generalremarks..........................61.3Datacompression.........................71.4Localadaptivity..........................91.5Nonlinearsmoothingproperties...

4、..............91.6Synopsis..............................102TheHaarbasiswaveletsystem173Theideaofmultiresolutionanalysis253.1Multiresolutionanalysis.....................253.2Waveletsystemconstruction...................273.3Anexample............................284SomefactsfromFourieranalysis315Basic

5、relationsofwavelettheory355.1Whendowehaveawaveletexpansion?.............355.2Howtoconstructmothersfromafather............425.3Additionalremarks........................446Constructionofwaveletbases476.1ConstructionstartingfromRieszbases.............476.2Constructionstartingfromm0..................5

6、47Compactlysupportedwavelets597.1Daubechies'construction.....................597.2Coi ets...............................63i7.3Symmlets.............................658WaveletsandApproximation698.1Introduction............................698.2SobolevSpaces..........................708.3Approximationk

7、ernels......................738.4ApproximationtheoreminSobolevspaces...........748.5Periodickernelsandprojectionoperators............798.6Momentconditionforprojectionkernels............828.7Momentconditioninthewa