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1、REPRODUCINGKERNELHILBERTSPACESathesissubmittedtothedepartmentofmathematicsandtheinstituteofengineeringandscienceofbilkentuniversityinpartialfulfillmentoftherequirementsforthedegreeofmasterofscienceByBaverOkutmu¸sturAugust,2005IcertifythatIhavereadthisthesisandthatinmy
2、opinionitisfullyadequate,inscopeandinquality,asathesisforthedegreeofMasterofScience.Assist.Prof.Dr.AurelianGheondea(Supervisor)IcertifythatIhavereadthisthesisandthatinmyopinionitisfullyadequate,inscopeandinquality,asathesisforthedegreeofMasterofScience.Prof.Dr.Mefhare
3、tKocatepeIcertifythatIhavereadthisthesisandthatinmyopinionitisfullyadequate,inscopeandinquality,asathesisforthedegreeofMasterofScience.Assoc.Prof.Dr.H.TurgayKaptano˘gluApprovedfortheInstituteofEngineeringandScience:Prof.Dr.MehmetB.BarayDirectoroftheInstituteEngineerin
4、gandScienceiiABSTRACTREPRODUCINGKERNELHILBERTSPACESBaverOkutmu¸sturM.S.inMathematicsSupervisor:Assist.Prof.Dr.AurelianGheondeaAugust,2005InthisthesiswemakeasurveyofthetheoryofreproducingkernelHilbertspacesassociatedwithpositivedefinitekernelsandweillustratetheirapplica
5、tionsforin-terpolationproblemsofNevanlinna-Picktype.FirstlywefocusonthepropertiesofreproducingkernelHilbertspaces,generationofnewspacesandrelationshipsbetweentheirkernelsandsometheoremsonextensionsoffunctionsandkernels.OneofthemostusefulreproducingkernelHilbertspaces,
6、theBergmanspace,isstudiedindetailsinchapter3.AftergivingabriefdefinitionofHardyspaces,wededicatethelastpartforapplicationsofinterpolationproblemsofNevanlinna-Picktypewiththreemaintheorems:interpolationwithafinitenumberofpoints,interpolationwithaninfinitenumberofpointsand
7、interpolationwithpointsontheboundary.FinallyweincludeanAppendixthatcontainsabriefrecallofthemainresultsfromfunctionalanalysisandoperatortheory.Keywords:Reproducingkernel,ReproducingkernelHilbertspaces,Bergmanspaces,Hardyspaces,Interpolation,Riesztheorem.iiiOZET¨DOGURA
8、NC¸EK˘IRDEKL˙IH˙ILBERTUZAYLARI˙BaverOkutmu¸sturMatematik,Y¨uksekLisansTezY¨oneticisi:Yrd.Do¸c.Dr.AurelianGheondeaA˘gustos,20
