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1、LectureNotesinMathematics1863Editors:J.--M.Morel,CachanF.Takens,GroningenB.Teissier,ParisHartmutFuhr¨AbstractHarmonicAnalysisofContinuousWaveletTransforms123AuthorHartmutFuhr¨InstituteofBiomathematicsandBiometryGSF-NationalResearchCenterforEnvironmentandHealthIngolstadterLandstr
2、asse¨185764NeuherbergGermanye-mail:fuehr@gsf.deLibraryofCongressControlNumber:2004117184MathematicsSubjectClassification(2000):43A30;42C40;43A80ISSN0075-8434ISBN3-540-24259-7SpringerBerlinHeidelbergNewYorkDOI:10.1007/b104912Thisworkissubjecttocopyright.Allrightsarereserved,wheth
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4、CopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediahttp://www.springeronline.comcSpringer-VerlagBerlinHeidelberg2005Print
5、edinGermanyTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Typesetting:Camera-readyTEXoutputbytheautho
6、rs41/3142/du-543210-Printedonacid-freepaperPrefaceThisvolumediscussesaconstructionsituatedattheintersectionoftwodiffer-entmathematicalfields:Abstractharmonicanalysis,understoodasthetheoryofgrouprepresentationsandtheirdecompositionintoirreduciblesontheonehand,andwavelet(andrelated)
7、transformsontheother.Inasensethevolumereexaminesoneoftherootsofwaveletanalysis:Thepaper[60]byGrossmann,MorletandPaulmaybeconsideredasoneoftheinitialsourcesofwavelettheory,yetitdealswithaunitaryrepresentationoftheaffinegroup,citingresultsondiscreteseriesrepresentationsofnonunimodul
8、argroupsduetoDu-floandMoore.Itwasalsoobservedin[